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HONORS CALCULUS
Final Exam Review (Page 1)
1. Find: lim
x 0
NAME__________________________
f  x  x   f  x 
x
2. Find the natural domain of :
if
f  x 
f  x  x 2  1
2x 2  x  3
x 2  3x  2
3 , x  0

3. Graph the function : f  x   2 x , 0  x  4
2 x  10 , x  4

4. . Graph the following and find the range and the zeros of each:
f(x) = x 2 - 4x + 2
[ - 1, 3 ]
a. range: ___________________
zeros: ___________________
5. Evaluate each limit
x
a. lim
x  0 sin 7 x
x  5 x  3

b. lim f ( x)  6 x  3
x 3
2 x x  3

c.
x 2
d. lim
x 2
e.
f.
( y  1)( y  2)
y 1
lim
lim
x2  4x  4
x2  x  6
x 
3
y4
4 x
x 4 2 
x
h. lim
i.
6  x3
lim 3
x  7 x  3
j.
lim
x
3
sin x
2 cos 2 x
tan 4 x
x 0
2x
k. lim
5x2  7
x  3 x 2  x
lim
x
g. lim 2
x2 x  4

l.
3
4

lim 4 4  x
x 0
x
6. Find an equation of the tangent line to the graph of f ( x)   x 3  3x  1  x  2  at
the point ( 1, -3 )
7.
8.
f ( x)  3x3  4 x 2  1 find f ''( 2)
Find the equation of the line normal to the curve y = 2 x 2  3x  1 at the point
on the curve where x = 1.
HONORS CALCULUS
Final Exam Review (Page 2)
NAME__________________________
9. Determine whether the following functions are continuous or discontinuous. If
the function is discontinuous, determine the point(s) of discontinuity and state if
the discontinuity is removable or non-removable.
2 x 2  5 x  12
a. f ( x) 
3x  12
3x  6
x  3x  2
b.
f ( x) 
c.
2 x  1 x  3
f ( x)   2
 x 1 x  3
d.
f ( x)  cos x  4
2
10. Find the derivative of each function.
a.
b.
c.
1
f ( x)  x 2  cos x
2
f ( x) 
x3  3x 2  4
x2
d.
f ( x) 
e.
f ( x)  2sin x  3cos x
2
3x 2
2

f ( x)  3x  x 2  
x

11. A ball is thrown straight down from the top of a 220 foot building with an initial
velocity of -22 feet per second. What is its velocity after 3 seconds? What is its
velocity after falling 108 feet?
12. A projectile is shot upward from the earth’s surface with an initial velocity of 384
feet per second. What is its velocity after 5 seconds? After 10 seconds? What is
the maximum height the object can reach?
13. Identify all intercepts, find any asymptotes, and sketch the graph
x2
a. f ( x)  2
x 9
x3
b. g ( x)  2
2x  8
3
2
14. f  x   x  ax  bx  c 

f  2  1


f '  3  49


f ''  3  24

Find f  7 