Mercer County Community College
Prof. Porter
MAT151
NAME:____________________
1. What is Calculus?
Answer:____________________
What is the derivative?
Answer:____________________
What 3 conditions are required for continuity?
2. Given the data (1,5), (2,7), (3,10):
Find the average rate of change between x=1 and x=3
Answer:____________________
Find the exponential regression
Answer:____________________
Find the instantaneous rate of change of your regression at x = 2
Answer:____________________
3. Find
lim5 x  7
x2
Answer:____________________
Use the δ-ε definition of limits to show
lim5 x  7 exists.
x2
Answer:___________________
Exam 1
4. Evaluate the limit:
x2  5x  6
lim
x2  4
x2
Answer:___________________
5.
x2  5x  6
When the function is continuous . f ( x) 
x2  4
Answer:____________________
Where is the function removably discontinuous?
Answer:____________________
Graph the function:
6. Evaluate
lim
x 0
sin( x)
sin( x)
by finding the values of f(x) =
at x = .1, .01, and .001
x
x
Answer:____________________
Evaluate
lim
x 3
x 1  2
x 3
Answer:____________________
7. Use the definition of derivative to find f ’(x)if f(x) = x2+ 3x - 12
Be sure to give f(x+h) clearly.
Answer:____________________________
(No credit for just answer- must use definition!)
8. P(t) = t (5 – 2t) + 7 represents the height of a ball at time t.
Evaluate the function at 0 and 1 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:_________________
9.
Given the graph and table. Evaluate the limit
lim f ( x)
x a 
a=
1
2
3
4
∞
lim f ( x)
x a 
10. Given the same graph above, determine y’(x)approximately at 1, 2, 3,4 etc
X=
1
2
3
4
∞
f’(x)
11. Find dy/dx of the following:
f ( x)  x  cos(2 / 7)
f ( x)  sin( x)  tan( / 2)
Answer:____________________________
Answer:____________________________
cos( x)
f ( x) 
ex
Answer:____________________________
12. Find y’(0)for and y’’(0)
f ( x)  xe x
Answer:_____________________________
 Ax  5 x  1
13. Given the function, find A so that the function is continuous: f ( x)   2
x  2 x 1
Answer:____________________
Give a qualitative graph of the continuous function.
14. Evaluate the limits.
3x 200  5 x  6
x 
5 x 2000  9
a. lim
Answer:____________________
3x 200  5 x  6
x 
5 x 200  9
b. lim
Answer:____________________
c. lim
x 
3x
 5x  6
5x  9
2000
200