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Summer Assignment – for the future AP Calculus BC Students ONLY!
Name___________________Score_____
Calculus Warm-up # 1-A
NO CALCULATORS THIS WEEK!
1) Find the domain of the function
f(x) = x  3
________
Name_____________________Score_____
Calculus Warm-up # 1-B
NO CALCULATORS THIS WEEK!
6) Find the value of 4
1
2) ) Find the domain of the function
f(x) = x  3
________
3) For what value of x is the function
17
y=
undefined?
________
3 x
4) What is the y-intercept of the graph of
13  2 x
the function y =
?
________
x7
5) True or False? -32 = | -32| ________
Name___________________Score_____
Calculus Warm-up # 1-C
NO CALCULATORS THIS WEEK!
11) If f(x) = x2 – 7x + 12, find f(-5).
________
12) If f(x) = (x – 3)(x – 4), find f(12).
________
13) Find the domain of the function
y = x5.
________
7) True or False? 25
3
2
_________
2
= -5 _________
8) Find the domain of the function
y= x
_________
9) Find the domain of the function
y = ( x  7)
3
2
_________
10) Find the range of the function
y = 2x.
________
Name_____________________Score_____
Calculus Warm-up #1-D
NO CALCULATORS THIS WEEK!
16) At what point, besides the origin, do the
graphs of y = x2 and y = x3 intersect?
________
17) True or False? If x is any Real number,
then
x 2  25 is also a Real number.
________
2
18) Find f(5) if f(x) = x – 8x + 15
________
14) Find the domain of the function
1
y=
.
________
x5
19) Find f(5) if f(x) = (x – 3)(x – 5)
________
15) For what values of x is the function
x
f(x) = 2
undefined? ________
x 1
20) True or False? If x = -3,
then
x 2  7 = | x - 1|
________
Name___________________Score_____ Name_____________________Score_____
Calculus Warm-up # 2-A
NO CALCULATORS THIS WEEK!
1) Find the domain of the function
x2  7
f(x) = 2
________
x  25
2) ) Find the domain of the function
x2  2
f(x) = 2
________
x  25
3) True or False? If x  R , then x 2  25
is always positive.
________
4) For what value of x is the function
x2  4
f(x) =
undefined?
________
x2
5) sin ( 7π/6) =
________
Calculus Warm-up # 2-B
NO CALCULATORS THIS WEEK!
6) True or False? If x > π/2, then
sin 12x > 1.
_________
7) True or False? y   sin x is a reflection
of the sine graph about the x-axis. _________
8) For what value of x is the function
6x
f(x) =
undefined in the interval
sin x
[π/2, 3π/2] ?
_________
9) Find the domain of the function
_________
f ( x)  9  x 2
10) cos (3π/2) =
________
Name___________________Score_____ Name_____________________Score_____
Calculus Warm-up # 2-C
NO CALCULATORS THIS WEEK!
11) On what interval is the function
f ( x)  9  x defined?
2
_________
12) Find the x-intercept of the function
x7
f ( x)  2
____________
x  6x  8
Calculus Warm-up # 2-D
NO CALCULATORS THIS WEEK!
16) Find the value of (-8)1/3
_________
17) Multiple Choice.
What is the value of -41/2?
D. -1/2
________
18) True or False? Given that y = 1/x,
13) Find the slope of the line whose
if x > 100, y < .01
_________
equation is 6x + 3y = 11.
__________
14) Find the slope of the line that goes
through (7, 2) and (-1, 0) __________
15) tan (3π/4) =
_________
A. -2
B. dne
C. 2
19) Multiple Choice. How does the graph of
f(x) - 7 compare to the graph of f(x)?
A. slide 7 units up
B. slide 7 units left
C. slide 7 units down D. slide 7 units right
________
20) csc (2π/3) =
________
Name___________________Score_____
Calculus Warm-up # 3-A
NO CALCULATORS TODAY
1) sin (-3π/2)
________
2) Is the function f(x) = 6x2 a one-to-one
function?
________
3) Find the inverse of the function
f(x) = x2 + 5, where x ≥ 0 ________
4) Find the domain of the function
x 5
________
y
x4
5) Find the y-intercept of the graph of
y = ex + 5
________
Name_____________________Score_____
Calculus Warm-up # 3-B
NO CALCULATORS TODAY
6) True or False? If f and g are nonzero
functions, then f(g(x)) = g(f(x)).
_________
7) At how many points do the graphs of
y = 3x3 + 1 and y = 3x3 + 6 intersect?
_________
8) For what value of x between π and 3π is
5x
y
undefined? _________
cos x  1
9) Write the equation of the line with slope
7 that passes through the point (6, -2).
_________
6 4
10) Simplify:
Name___________________Score_____
Calculus Warm-up # 3-C
NO CALCULATORS TODAY
11) If f(x) =
x3  x
, find f(3).
x2  1
x2
_________
Name_____________________Score_____
Calculus Warm-up #3-D
CALCULATORS ARE ALLOWED
16) Is the function y  2 x7  3x5  x  2
________
12) Find f(-3) for the function above.
________
13) Is the function referred to above an
even function, an odd function, or
neither?
________
14) sec (2π/3)
x 
________
15) Find the vertical asymptote of the
3
graph of the function f ( x)  x
2 1
________
an even function, an odd function, or
neither?
________
17) Is the above function one-to-one?
________
18) If the graph of f(x) = x2 is shifted two
units to the right to form g(x), what
would be the equation of g(x)?
________
19) Write the equation of the line through
the point (-9, 2) that is parallel to
2x – 5y = 16
________
20) Simplify: (x – 2y)2 – (xy2 – y2)
________
Name___________________Score_____
Calculus Warm-up # 4-A
NO CALCULATORS THIS WEEK!
Name_____________________Score_____
Calculus Warm-up # 4-B
NO CALCULATORS THIS WEEK!
1) sin (π/2)
________
On # 6-9, Solve for x, when 0 ≤ x < 2π
2) cos (3π/4)
________
6) cos x = 0
_________
3) tan (-π/4)
________
7) sin x = -1/2
_________
4) sec (π/3)
________
8) sec x = 2
_________
9) tan x = 1
_________
5) Simplify:
(2x2)3
x10
____________
Name___________________Score_____
Calculus Warm-up # 4-C
NO CALCULATORS THIS WEEK!
11) tan (5π/4)
_______
12) cos (-π)
_______
13) csc (π)
_______
14) sin ( -5π/3)
_______
15) Does y = │x3 - x│ have even or
odd symmetry?
___________
3x
x  5x
___________
10) Find the domain of y =
2
Name_____________________Score_____
Calculus Warm-up # 4-D
NO CALCULATORS THIS WEEK!
On #16-18, solve for x when 0 ≤ x < 2π.
16) sin x =
2
2
17) cos x =
3
2
18) csc x = -1
_________
_________
_________
19) What is the domain of y = tan x?
___________
20) Write the equation of the line
through (9, -4) and ( -1, 5)
___________________
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 5-B
NO CALCULATORS THIS WEEK!
Calculus Warm-up # 5-A
NO CALCULATORS THIS WEEK!
1) lim  3x 2  4 
x 2
2) lim  2
x3
x

________
6) Find f(4) if f(x) = x + 5
_________
________
x 2  25
7) Find f(4) if f(x) =
x 5
________
3) lim cos 2 x
________
4) lim x
________
x 0
x 0
5) Write the equation of the vertical line
through the point (-6, 8).
________________
Name___________________Score_____
Calculus Warm-up # 5-C
NO CALCULATORS THIS WEEK!
8) For what value of x is f(x) =
undefined?
x 2  25
x 5
_________
x 2  25
x 5
x 4
=
_______
x 2  25
10) x 5 x 5
=
_______
9)
lim
lim
Name_____________________Score_____
Calculus Warm-up # 5-D
NO CALCULATORS THIS WEEK!
16) Is the function y = x continuous
11)
12)
lim f ( x ) =
_______
lim f ( x) =
_______
x b 
x b 
13) True or False? lim
x b
14)
lim f ( x ) =
x c
f ( x ) does not exist.
_______
15) True or False?
lim f ( x) = lim f ( x)
x c
x c 
at x = 7.2.
_________
2
 x  3, x  2
17) Is f(x) = 
continuous
 9  x, x  2
at x = 2?
__________
18) Is the function y = │x - 2│ continuous
at x = 2 ?
__________
19) Is the function y =
at x = 2?
x 2
20) x 0 x 2  4
lim
x2
continuous
x2  4
__________
=
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 6-B
NO CALCULATORS THIS WEEK!
Calculus Warm-up # 6-A
NO CALCULATORS THIS WEEK!
x5

x 5 x 2  25
_______
6) lim
2) lim
x5

x 2  25
_______
7)
3) lim
x 5

x 2  25
_______
8) lim
7

x
_________
________
9) lim
7

x7
_______
___________
10) Multiple Choice: lim  x 2  
1) lim
x 5
x 5
x 5

x  x 2  25
4) lim
x 2  25
5) lim

x 0 x  25
7

x  x
lim
x 
x 0
x 7
Calculus Warm-up # 6-C
NO CALCULATORS THIS WEEK!
11) True or False?
x  49
approaches
x7
98 as x approaches 7.
The function f(x) =
2
10

x 10 x
______
10

x  x
______
13) lim
10
14) lim 
x 0 x
______
15) Find the slope of a line perpendicular
to the line y = 6x – 1.
______
________
x 7
B. 49
C.
1
49
D.
1
14
Name_____________________Score_____
Calculus Warm-up # 6-D
NO CALCULATORS THIS WEEK!
16) What is the slope of a line perpendicular
to the line 3y + 5x = 10?
______
17) lim
x 6
12) lim
1000

x2
A. -14
Name___________________Score_____
________
x6

x6
______
18) What is the image of the point (-2, 7)
when it is reflected across the x-axis?
_______
19) Multiple Choice:
A. x a b
B. x ab
x 
a b

C. x a
b
D.  x a  xb 
20) Find the y-intercept of the function
g(x) = 5 cos 2x
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 7-B
NO CALCULATORS TODAY!
Calculus Warm-up # 7-A
NO CALCULATORS TODAY!
1) Find the domain of the function
7
f(x) =
x2
2) Does the graph of y =
_______
8) lim
5x2

x  6 x 2
_______
5x2
9) lim 5 
x  6 x
_______
5) If y  (3x 2  2)6 , find y’.
_______
x2  1
is
2x
_______
_______________
Name___________________Score_____
Calculus Warm-up # 7-C
NO CALCULATORS TODAY!
______
x 0
13) lim cos x 
x

2
1

x  0 sin x
14) lim
10) If y 
5
, find y’.
( x  2 x) 2
3
______
Calculus Warm-up # 7-D
USE YOUR TI-89 TODAY! Round to 3 decimal places.
1
1  2 1/ x
16) Find lim f ( x) 
_______
17) Find lim f ( x) 
_______
18) Find lim f ( x) 
_______
19) Find lim f ( x) 
_______
x 
______
____________
Name_____________________Score_____
Let f(x) =
4
12) lim tan x 
_______
x2  9
have a hole
x4
undefined when x = -1/2.

5x2

x 0 6 x 2
_______
4) True or False? The function y =
x
lim
7)
or an asymptote at x = 4?
11) lim sin x 
_______
x2  9
have a hole
x 3
or an asymptote at x = 3?
3) Does the graph of y =
5x2

x 0 6 x
6) lim
x 
x 0
______
x 0
15) If f ( x)  3cos4 (5x) , find f '( x)
____________
20) Find f '(1)
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 8-B
NO CALCULATORS TODAY!
Calculus Warm-up # 8-A
NO CALCULATORS TODAY!
1) If u = 3x4, find
2) If v = 5x3, find
du
dx
dv
dx
6) If u = 6x5, find
_______
7) If v = 3x3, find
3) Multiply u ∙ v, and simplify it.
Call the product y.
y = _______
dy
4) Find
dx
du
dx
_______
dv
dx
u
, and simplify it.
v
Call the quotient y.
_______
8) Find
_______
9)
du
dv
and
from # 1 and # 2.
dx
dx
Is it true that (uv)′ = (u′)(v′)? ______
_______
Find
y = _______
dy
dx
_______
5) Multiply
Name___________________Score_____
Calculus Warm-up # 8-C
NO CALCULATORS TODAY!
11) Where does the graph y =
a hole?
x 2  36
have
x6
_________
 u  u 
10) Is it true that    ?
 v  v
_______
Name_____________________Score_____
Calculus Warm-up # 8-D
USE YOUR TI-89 TODAY! Round to 3 decimal places.
Given f(x) =
4
e 1
2x
16) Find lim f ( x)
_______
12) Write the equation of the tangent line
to y = x3 – 4x at the point (1, -3).
_________
17) Find
_______
13) Find the slope of the tangent line to
y = 2x4 + x – 1 where x = 2
______
18) Find f (ln 2)
_______
14) Find the slope of a line which is
parallel to the line 2y = 7x - 6 ______
19) Find f ′ (ln 2)
_______
20) Find f ′′ (ln 2)
_______
15) Find the y-intercept of the graph of
f(x) = 3x5 + x4 – 2x3 -7x + 6 ______
x 0
lim f ( x)
x 
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 9-B
NO CALCULATORS TODAY!
Calculus Warm-up # 9-A
NO CALCULATORS TODAY!
1) Find
dy
5
if y  6x 5 
x
dx
_______
6) Find y ′ if y  x 4 (7 x 2  1)
7) Find y ′ if y 
5x2  2
x
_______
_______
2) Find
dy
if y  7  3x 4  x
dx
_______
3) Find
dy
if y 
dx
x
_______
8) Find y ′ if y  800 x
_______
4) Find
dy
if y  4 x5
dx
_______
9)
_______
5) What is the vertical asymptote of the
17  x
function g ( x) 
?
_______
x4
Name___________________Score_____
Calculus Warm-up # 9-C
NO CALCULATORS TODAY!
Find y ′ if y  732
10) The graph of f(x + 4) is a translation of
the graph of f(x) 4 units in which
direction?
_______
Name_____________________Score_____
Calculus Warm-up # 9-D
USE YOUR TI-89 TODAY! Round to 3 decimal places.
11) Find
dy
6x2
if y 
dx
x 3
_______
16) True or False? For all x,
x12  73 x  19  5
12) Find
dy
9
if y  5
dx
x
_______
17) Find the domain of the function
y
dy
13) Find
if y  (6 x2  9)4
dx
_______
dy
1
14) Find
if y  2
dx
x3
_______
15) Find the slope of the curve
y  x3  7 x  2 where x = -2
x 2  25
x2  4
18) Find f (0) if f ( x)  6e2 x
19) Find
lim
x 0
_______
cos x
x
_______
_______
_______
_______
20) Find the slope of the curve
_______
y  xe x where x = 1
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 10-B
NO CALCULATORS TODAY!
Calculus Warm-up # 10-A
NO CALCULATORS TODAY!
1) Find
dy
if y  9 x  5
dx
dy
2) Find
if y  9x5
dx
dy
9x
3) Find
if y 
5
dx
dy
4) Find
if y  5 x9
dx
_______
_______
_______
Name___________________Score_____
dy
12) Find
if y  tan  x  2 
dx
7) Find y ′ if y  e4 x
_______
8) Find y ′ if y  e 4
_______
9)
_______
Find y ′ if y  4 x  e x
10) What is the y-intercept of the graph
of y  e x ?
_______
Name_____________________Score_____
Calculus Warm-up # 10-C
NO CALCULATORS TODAY!
dy
if y  cos 2x
dx
_______
_______
5) What is the domain of the function
________
y  ex ?
11) Find
6) Find y ′ if y  x 4
Calculus Warm-up # 10-D
NO CALCULATORS TODAY!
__________ 16) Find log4 8
17) Find log 25 1
_________
_______
_______
19) Solve: log3 (2 x  1)  4
_______
dy
if y  e x sin x
dx
__________
14) Find
dy
x
if y 
cos x
dx
___________
____________
5
18) Solve: 2 x  2  8 x
13) Find
15) Write the equation of the tangent line
to the curve y  sin 2 x at x  
2
_______
20) What is the domain of y  ln x ?
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 11-A
USE YOUR TI-89 TODAY! Round to 3 decimal places
1) log4 64 =
_______
2) log7 252 =
_______
3) Find x if log3 x = 5.
_______
4) Find x if log4 (2x – 1) = 7
_______
Calculus Warm-up # 11-B
NO CALCULATORS TODAY!
6) Find x if log2 8 = x
3x
x
7) Find x if 4  2
2
_______
8
_______
8) Find x if log3 x = 2
5) Find x if 23x = e5.
_______
_______
9) Find x if log4(2x-3) = 2
__________
10) True or False: The slope of the curve
y = ln x is always positive.
_______
Name___________________Score_____
Calculus Warm-up # 11-C
NO CALCULATORS TODAY!
dy
11) Find dx if y  ln 5x
dy
12) Find dx if y  log3 15x
dy
13) Find dx if y  log4 (2 x  3)
Name_____________________Score_____
Calculus Warm-up # 11-D
NO CALCULATORS TODAY!
_______
dy
16) Find dx if y  ln (8x2)
_______
_______
dy
17) Find dx if y  sin(2x)
_______
_______
dy
x2  3
y  ln
x4
14) Find dx if
dy
18) Find dx if y  e sin(2x)
dy
sin 2 x
19) Find dx if y  ln e
_______
_______
________
15) Find the domain of f-1(x) if
f(x) = ln x + 2
20) What is the domain of g-1(x)
if g ( x)  ln( x  2) ?
_______
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 12-A
NO CALCULATORS TODAY!
Calculus Warm-up # 12-B
NO CALCULATORS TODAY!
2
6) Find f ( x ) if f ( x)  x cos x
f ( x)  1
x
1) Find f (3) if
_______
2) Find f ( ) if f ( x)  sin x
_______
7) Find f ( x ) if
3) Find f (0) if f ( x)  e
_______
2
5
8) Find f ( x ) if f ( x)  (3x  1)
_____________
f ( x) 
x 1
x2
_________
__________
5x
lim
4) Find
x2
x2
x  x6
2
_______
lim
9) Find
5) Write the equation of the tangent
line to the curve y = 5x2- 2x at x = -1
____________
Name___________________Score_____
11) Find
x2
sin x
x
Name_____________________Score_____
Calculus Warm-up # 12-D
NO CALCULATORS TODAY!
16) Find f (2) if f ( x)  ln x
x2
x2  4
_______
10) Write the equation of the tangent line
to the curve y = 3x5- x3 at x = -1
______________
Calculus Warm-up # 12-C
Use your TI-89 TODAY! Round to 3 decimal places
lim
x 0
_______
_______
x2
2
12) Find x  x  4
17) Find
lim
_______
f ( )
2 if f ( x)  3sin 2 x _______
2 x4
x
18) Find x 0
lim
13) Find f (2) if f ( x)  e
_______
3
14) Find f ( ) if f ( x)  sin(2 x ) _______
tan( x  h)  tan x

h
15) h0
_______
x2
3x 4  6 x  1
4
19) x  5 x  4
lim
lim
20)
lim
_______
x 2
x 4  24
x2
_______
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 13-A
NO CALCULATORS TODAY!
2
4
1) If y  (6 x  9) , find
Calculus Warm-up # 13-B
NO CALCULATORS TODAY!
3
3
6) Find y if y  4(2 x  1)
dy
dx
__________
2) For what value of x is the function
7
f ( x) 
( x  3)5 undefined?
___________
7
f ( x) 
( x  3)5 , find f ( x )
3) If
y  (sin x) , find
6
4) If
5) If y  sin 6 x , find
2
7) Find y if y  cos(7 x )
_____________
2
8) Find y if y  (cos 7 x)
_____________
___________
9) Find y if y  tan 3 x
dy
dx
___________
___________
dy
dx
_____________
___________
Name___________________Score_____
10) Find a possible formula for f ( x) if
f ( x)  sec2 x
_____________
Name_____________________Score_____
Calculus Warm-up # 13-C
Calculus Warm-up # 13-D
NO CALCULATORS TODAY!
Answer True or False based on the graph below.
dy
16) Find
dy
17) Find
dy
11) f ( x) is continuous at x = g.
12) f (a )  0
________
_______
13) f ( x) is differentiable at x = d
________
14) f ( x) is differentiable at x = g
________
15) f (c)  f (h)
_______
18) Find
sin 2 x
dx if y  e
__________
2
dx if y  sec(4 x  x )
_______________
2
dx if y  sec 4 x  x
____________________

f
(
x
)

cos
x
19) If
, find a possible formula
f
(
x
)
for
.
_______
2
20) For what value of x does the curve y  3x  7 x
have a horizontal tangent line?
_______
Name___________________Score_____
Calculus Warm-up # 14-A
NO CALCULATORS TODAY!
1) If y  e
Calculus Warm-up # 14-B
NO CALCULATORS TODAY!
dy
6x3
, find
dx
Name_____________________Score_____
__________
2
6) Find y if y  x tan x
_____________
cos x
x
7) Multiple Choice:
a) 1
b) 0
c) -1
d) dne
lim
2) Is f (9) undefined if f ( x)  x  9 ? ________
3) Is f (9) undefined if f ( x)  x  9 ? ________
4) If
y  2 x5  1 , find
x 0
8) Multiple Choice:
dy
dx _____________
a) 1
b) 0
3x  2 x
lim
2
9) x 5 x  3
lim tan x
x 0

c) 2
_____
_____
d) dne
2
2
dy
y
( x  1)3 , find
dx
5) If
_______________
Name___________________Score_____
Calculus Warm-up # 14-C
______
10) Find the slope of the tangent line to the circle
x 2  y 2  25 at the point (3, 4)
______
Name_____________________Score_____
Calculus Warm-up # 14-D
NO CALCULATORS TODAY!
Use the graphs to find the value of each.
16) Find the x-intercepts of the function
y  2 x 4  32 x 2
__________
17) If f ( x)  x , does f ( x) ever have a
horizontal tangent?
3
2
18) If y  2 y  7 x  4 , find
11) a
12) b
______
________
14) d
________
_______
dx
_____________
dy
19) Find
15) g
dy
________
13) c
______
dx if y  sin( x  2)
_____________
20) Which function has a constant 2nd derivative?
x
2
a) y  e
b) y  3x  4 x  9
c) y  ln x
3
d) y  x  1
______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 15-A
NO CALCULATORS TODAY!
3x 2  2 x5
5
1) x  5 x  3
Calculus Warm-up # 15-B
NO CALCULATORS TODAY!
lim
lim
sin 2 x
2) If y  e
, find
3) 
3
1
______
dy
dx
____________
x 2  3 dx
2
4) cos(
6)
2x
7) If y  7 , find
_______
8)
3)=
x 4

3
1
Name___________________Score_____
1
x 3
x 3
2
5
12) If y  ( x  7) , find
14)
csc  3 / 4
dx
_____________
1
dx
x2
______
10) If
V  43  r 3
______
dV
, find
dt
_______________
Name_____________________Score_____
Calculus Warm-up # 15-D
NO CALCULATORS TODAY!
_______
dy
dx
_____________
16)
lim
x4
x 1
x4

2
2
4  x 2 dx
________________
19) arctan(-1)
_______
3
15) On what intervals is f ( x)  x  3x  5
increasing?
______________
_________
4
17) If y  ln (5 x ) , find
18)
2
x
dx
3

x 1
13)
dy
1
9) arcsin (- 2 )
Calculus Warm-up # 15-C
NO CALCULATORS TODAY!
11)
_______
________
1
y
x where
5) Find the slope of the curve
x = 5.
_______
lim
x2  4 x
x 2  3x  4
dy
dx
__________
Hint: Use geometry!
_______
_________
20) True or False: If f ( x) has a relative
maximum at x  p , then f ( p)  0 .
_______
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 16-A
Answer True or False based on the graph below.
Calculus Warm-up # 16-B
NO CALCULATORS TODAY!
2
6) If A   r , find
7) True or False:
1) f ( x) has a relative maximum at b .
________
y
8) If
x
dA
3
5
dt

___________
 x
3
5
_______
x
dy
x  3 , find
dx
2
___________
2) f ( x) has an absolute maximum at b .________
3) If a  r  b, then f (r )  f (b)
4) f (c)  0
5)
lim f ( x )
x c
________
x 9
0
2
9) Solve for x: x  3
________
3
10) If y  2 y  7  16 x, find
does not exist.
______
dy
dx
_______
_______________
Name___________________Score_____
Calculus Warm-up # 16-C
NO CALCULATORS TODAY!
11) Draw a curve that is increasing and concave up.
__________
6x
12) 
13)
2
 10 x  7 dx
15)
 7e
x
dx
Calculus Warm-up # 16-D
NO CALCULATORS TODAY!
3
16) If f ( x)  9  8 x , find f ( x)
_________
y  ln (sin x) , find
_________________ 17) If
  sin x dx
x
14) If y  e ln x, find
Name_____________________Score_____
______________
dy
dx
______________
dy
dx
__________
18) True or False: If f (b ) exists and f (b)  0,
there must be a horizontal tangent at x  b.
________
16
6
19) True or False: If f ( x)  x  2 x , then
f (17)  f (17)
__________
______________
20) True or False: The function
differentiable at x = 2.
y  x2  4
is
__________
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 17-A
NO CALCULATORS TODAY!
5
1) If y  3x  2 x  1 , find y ( x )
2) If f ( x)  ln x , find f ( x)
x
3) If y  xe , find
Calculus Warm-up # 17-B
NO CALCULATORS TODAY!
3x 2
 3 dx
4) x  1
sin x
cos x dx
6)
____________
7) Find the domain of the function
x 1
f ( x) 
x
____________
8) Find the vertical asymptote of the function
2x  5
f ( x) 
3x  6
__________
sin x
lim
9) x 0 3 x
______
dy
dx
e
___________
___________
__________
5) If the position of a particle at time t is given by
3
2
the function s(t )  4t  5t  6t  1, find the
particle’s acceleration at t  2 .
_______
10) If the position of a particle at time t is given by
the function s(t )  sin 4t  2t , find the
particle’s velocity at
Name___________________Score_____
11)
2
0
3x2  4 dx
tan x dx  sec x  C
14) Evaluate:

1
x dx
 arctan x dx
0
________
2
________
2
4
_______
1
16)
5x
13) If f ( x)  e , find f (2)
3.
Calculus Warm-up # 17-D
CALCULATORS ALLOWED
Get decimal answers and round to 3 decimal places
________
12) True or False: 
t 
Name_____________________Score_____
Calculus Warm-up # 17-C
NO CALCULATORS TODAY!

___________
__________
 2
lim 1  
x 
 x
17)
x
2
x
18) Solve for x: x  e
_________
15) If the velocity of a particle at time t is given by
2
the function v(t )  t  2t  1 , find the net
change in position from t  0 to t  3 .
_______
5x2
f ( x)  3
x  1 , find f (9)
19) If
__________
__________
__________
20) If the velocity of a particle at time t is given by
2
the function v(t )  t  2t  1 , find the total distance
traveled from t  0 to t  3 .
___________
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 18-A
NO CALCULATORS TODAY!
1) If sin  5x , find d / dt
2)
2
0  2 x  3 dx
3
3) If y  2 x sin x , find
4)
___________
____________
Calculus Warm-up # 18-B
NO CALCULATORS TODAY!
3
Given: f ( x)  x  12 x  1
6) Find f (1)
f (3)
7) Find
dy
dx
 cos(5 x  1) dx
___________
__________
5) If the position of a particle at time t is given by
1
s (t )  t 3  4t 2  12t  3
3
the function
, find the
time interval when the particle is moving to the
left.
_______
Name___________________Score_____
12) If the Trapezoid Rule is used to approximate
2
the area under a portion of y  4  x , will it
_______
8) Find the slope of the secant line that goes
through the points you found in #6 and #7.
________
9) For what value of c in the interval (1, 3) is the
slope of the tangent line drawn at x = c equal to
the slope you found in #8 ?
________
x
10) x 0 sin x
lim
________
Name_____________________Score_____
Calculus Warm-up # 18-C
NO CALCULATORS TODAY!
2
11) Is the graph of y  4  x concave upward or
concave downward?
________
_______
Calculus Warm-up # 18-D
NO CALCULATORS TODAY!
Given:
16)

8
f ( x)dx  40
1
Find 
8

8

5
be an overestimate or underestimate?________ 17) Find
1
y
x concave up or concave
13) Is the graph of
down on the interval (0,8) ?
________ 18) Find
5
1
1
and 
f ( x)dx
( f ( x)  3)dx
2 f ( x)dx
5
1
f ( x)dx  10
________
__________
__________
3
2
14) If the Trapezoid Rule is used to approximate
19) If f ( x)  x  3x , find f ( x )
__________
91
1 x dx , will it be an over- or an underestimate? 20) Write the equation of the tangent line to
________
f ( x)  x3  3x 2 at its point of inflection.
2
15) If y  tan 7 x , find dy / dx
___________
_______________
Name___________________Score_____
Name_____________________Score_____
Calculus Warm-up # 19-A
Answer True or False based on the graph below.
Calculus Warm-up # 19-B
NO CALCULATORS TODAY!
3
6) Find the average value of y  2 x on the
interval [0, 2].
_______
1)
2)
3)

c

a

b
dy
f ( x) dx  0
b
________
f ( x) dx  0
b
________
________
a
________
5) If f (d )  f ( g )  f (h)  0 and g  d  h  g ,
g
d
h
f ( x) dx   f ( x) dx
g

b

3
______
12) If f ( x)  2 x , what is f ( x ) ?
________
f ( x)  x

6
2
f ( x) dx  20
, then
  f ( x)  3 dx =
6
2
A. 23
B. 27
x 5
10) Multiple Choice: Which is equal to e ?
x
5
x 5
x 5
ln( x  5)
A. e  e
B. ln e
C. e e
D. e
_______
Answer TRUE or FALSE, based on the piecewise
 x 2  36
, if x  k

f ( x)   x  k
 2k
, if x  k

function
, then f (3) 
16) If k = 5, there is a vertical asymptote at x = 5.
C. 1
D. -1
________
________
dy
sin x
y

ln
e
14) Multiple Choice: If
, then dx =
cos x
sin x
A. sin x
B. cos x
C. e
D. e
_______
15) Multiple Choice: If
______
Calculus Warm-up # 19-D
NO CALCULATORS TODAY!
6 dx
13) Multiple Choice: If
A. 3
B. -3
a
Name_____________________Score_____
Calculus Warm-up # 19-C
NO CALCULATORS TODAY!
11)
c
f ( x) dx   f ( x)dx
_______
Name___________________Score_____
5
____________
e
8) Find the slope of the graph of y  2
when x = 2.
______
a
4) f (a )  0

then
dx if y  x ln 2 x
9) True or False: If a  b  c , then
c
f ( x) dx   f ( x) dx
a
7) Find
C. 33
D. 32
_______
17) If k = 5, f(x) is not continuous at x = 6.
________
18) If k = 5, f(6) = 10.
________
19) If k = 6, f(6) = 12
________
20) If k = 6, f(x) is continuous at x = 6.
________