Mercer County Community College Prof. Porter MAT151 Exam 1

 

NAME:____________________

 

1.      What is Calculus?

 

What is varying in calculus?

 

How can you tell if something is increasing or decreasing?

 

 

 

2.      Use the δ-ε definition of limits to show that (find δ if ε = .01 so that the difference between the limit and the function is less than ε when the x values are within δ of 2)

 

 

 

 

 

 

 

 

Answer:____________________

 

3.      Evaluate the limit:

 

 

 

 

 

 

 

 

Answer:____________________

Evaluate the more complicated limit:

 

 

 

 

 

Answer:____________________

 

 

 

4.      Explain on when the function is continuous .

 

 

 

 

Answer:____________________

 

Where is the function removably discontinuous?

 

 

 

Answer:____________________

 

Graph the function:

 

 

 

 

 

 

 

 

 

 

5.      Does the function have a zero on the interval [0,1] ?

 

 

 

Answer:____________________

 

How can you show this without solving or graphing the equation?

 

 

 

 

 

Find the zero to two decimal places.

 

 

 

 

 

 


Answer:________________________

 

 

 

 

6.      Given the graph and table. Evaluate the limit

 

a=

1

2

3

0

-∞

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.      Given the same graph above, determine f(x) approximately at 1, 2, 3, 0

X=

1

2

3

0

-∞

f(x)

 

 

 

 

 

 

 

 

 

 

 

 

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.      Use the definition of derivative to find f(x) if f(x) = 2x2+ 3x - 12

Be sure to give f(x+h) clearly.

 

 

 

 

 

 

 

 

 

 

 

 

Answer:____________________________

(No credit for just answer- must use definition!)

10.  Find f and f of the following:

 

 

 

 

 

 

 

Answer:____________________________

 

 

 

 

 

Answer:____________________________

 

Find f(0) for

 

 

 

 

 

 

 

 

 

Answer:_____________________________

 

 

 

 

 

11.  What is another way of saying the slope of the tangent line?

 

 

 

Find f(0) for the equation f(x) = x(x+1)

 

 

 

 

Find the equation of the line tangent to the curve y = x(x+1) + 100100 when x = 0 and y = 100100

 

 

 

 

 

 

 

 

 

 

 

 

Answer:____________________________

 

12.  In finding y for y = , put the rules in order of use (do not include if rule is not used):

 

Power Rule, Derivative of Sine, Chain Rule, Quotient Rule, Product Rule

 

 

 

 

 

 

 

Answer:____________________

 

Find y if y =

 

 

 

 

 

 

 

 

 

Answer:____________________