Download MAT 1613 TEST #1 Name

MTH 125
Calculus I
TEST #1
Sec. 1.3-2.3
Name______________________
September 14, 2010
Show all work.
1. The graph of the function f is given.
Use the graph of f to find the following:
(a) lim f ( x)
(d) lim f ( x)
(g) f (4)
(j) f (2)
(b) lim f ( x )
(e) lim f ( x)
(h) lim f ( x)
(k) lim f ( x )
(c) lim f ( x)
(f) lim f ( x )
(i) lim f ( x )
x 0
x 0
x2
x 
x 0
x4
x2
x 5
x 3
(l) Determine the numbers at which f is discontinuous and state the reason for the
discontinuity.
numbers
reason
(m) Give equations of vertical and horizontal asymptotes if there are any.
Find each limit. Show all work.:
2. lim
x 
6x
5  2x
3. lim
x 0
x
6x
2
4. lim(4 x  5x  6 x  10)
3
x 1
6. lim
x 2
8. lim
t 2
x 2  3x
x2
t2
t 5 3
2
2
z 3
5. lim
z 8 z  2 z
7. lim
x 3
3x 2  5 x  12
2 x2  9 x  9
1 1

2
x
9. lim
x 4
x4
10. Determine any numbers at which the given function is discontinuous and state the reason for
the discontinuity.
(a) f ( x) 
1
2
x 9
(b) f ( x) 
x2  6 x  8
2 x2  7 x  4
 x3  8
if x  2

11. Find the value of a that will make f ( x)   x  2
continuous for all x .
 a
if x  2

12. (a) Use the limit definition to find the slope of the tangent line to the graph of f ( x) 
x  1.
(b) Write an equation of the tangent line.
3
at
x2
13. Use the limit definition of the derivative to find f ( x ) for f ( x)  x 2  1 .
Find the derivative of each of the following functions and simplify.
14. f ( x)  3x 4  2 x3  4 x 2  5 x  9
15. y 
2 x2 4
 
9 x3 8
x
16. y  5sin x  4 cos x
17. An object is propelled vertically upward with an initial velocity of 39.2 meters per second.
The distance s (in meters) of the object from the ground after t seconds is s(t )  4.9t 2  39.2t .
(a) What is the velocity of the object at any time t ?
(b) When will the object reach its highest point?
(c) What is the maximum height?
(d) When will the object hit the ground?
(e) What is the velocity upon impact?
18. The graphs of three functions of f are shown below.
For each function, sketch graphs of f  on the same grid.