Mercer County Community College
Prof. Porter
MAT151
NAME:____________________
1. What is Calculus?
What is varying in calculus?
What is the derivative?
2. Use the δ-ε definition of limits to show that
lim4 x  3 is 11.
x2
Answer:____________________
3. Evaluate the limit:
lim
x 3
x 2  5x  6
x2  9
Answer:____________________
Explain on when the function is continuous . f ( x) 
x 2  5x  6
x2  9
Answer:____________________
When is the function removable discontinuous?
Answer:____________________
Sample Exam 1
 Ax  7 x  2
4. Given the function, find A so that the function is continuous: f ( x)   2
x2
 x
Answer:____________________
Give a qualitative graph of the continuous function.
5. Evaluate the limit
lim f ( x)
x a 
A
0
1
2
3
4
lim f ( x)
x a 
6. Given the same graph above, determine f’(x) approximately at 1, 2, 3, 0
X=
1
2
3
4
∞
f’(x)
∞
7. h(t) = t (2 – t) + 3 represents the height of a ball at time t.
Evaluate the function at 0 and 2 and use that information to find the average speed of the ball
between t = 0 and t = 2.
Answer:_________________
Find the instantaneous speed at t = 1 for this problem.
Answer:_________________
8. Use the definition of derivative to find f’(x) if f(x) = x( x + 1)
Be sure to give f(x+h) clearly.
Answer:____________________________
(No credit for just answer- must use definition!)
9. Find f’ of the following:
f ( x)  x sin( / 3)
Answer:____________________________
5cos( x)
f ( x) 
x4
Answer:___________________________
10. Find g’(x) g ( x)  x5e2 x
Answer:_____________________________
Find g’’(x)
Answer:___________________________
11. Find y’ if y =
sin(4 x  7)
Which rules did you use (be sure to name them)?
x
Rules:_____________________
Answer:____________________
Find y’ if y = (ln x)(sin (e )) Which rules did you use (be sure to name them)?
1
2x
Rules:_____________________
Answer:____________________
12. Evaluate the limits.
.9 x 20  5 x  6
a. lim
x 
x 20  9
Answer:____________________
.9 x 200  5 x  6
x 
x 20  9
b. lim
Answer:____________________
c. lim
.9 x  5 x  6
x 200  9
d. lim
.9 x  5 x  6
x 20  9
20
x 
Answer:____________________
21
x 
Answer:____________________