Mercer County Community College            Prof. Porter        MAT111  

Calculus Midterm

 

  1. What is Calculus?

 

 

How can you use it?

 

 

  1. In 1990 sales were $3 Billion, and in 1995 sales were up to $5 Billion. If sales climbed to $10 Billion in 2002, what do you expect the sales to be in 2003 using a linear regression?

 

 

 

 

 

 

 

Answer:____________________

 

  1. If the function s(t) is found to model distance at time t, find the average speed between time t = 0 and t = 2 and instantaneous speed at t = 1 if

 

 

 

 

 

Ave:____________________

 

 

 

Instantaneous:_________________

  1. Find y’ if y =

 

 

 

 

 

 

 

Answer:____________________

 

  1. Use logarithmic differentiation to find y’ if y =

 

 

 

 

 

 

 

 

 

 

Answer:____________________

 

  1. A spherical balloon is inflating at a rate of 3 cc per second. How fast is the radius growing when the radius is 5 cm?

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer:____________________

 

  1. Approximate the square root of 102 using differentials.

 

 

 

 

 

 

Answer:____________________

 

  1. Use the definition of derivative to find the derivative of the function.

 

 

 

 

 

 

 

 

 

 

  1. Evaluate the more complicated limits:

 

a.

 

 

 

 

 

Answer:____________________

 

b.

 

 

Answer:____________________

 

  1. Determine if the graph below is continuous, has a limit, has a derivative at the points specified.

X=

1

2

3

4

Continuous

 

 

 

 

Differentiable

 

 

 

 

Limit Value

From left