Math 2431 – Calculus I



Math 2431 – Calculus I

Summer 2003 – Test 1

NAME______________________________________

Part 1

Directions: Show all work – correct answers with only partial work may receive only partial credit. NO calculator may be used on this part.

1. (5 points). Use the limit definition of derivative to find [pic] for [pic].

2. (10 points). Find the following limits, if they exist:

a. [pic]

b. [pic]

c. [pic]

Part 2

Directions: Show all work – correct answers with only partial work may receive only partial credit. You may use a calculator on this part – explain how you used the calculator as part of your answer.

3. (10 points)

a. Find the linear approximation to [pic] at x = 4.

b. Use the linear approximation to find [pic].

4. (10 points) Let [pic]. Find

a. [pic]

b. [pic]

c. [pic]

5. (10 points) Consider the function

[pic]

a. Find the values of a and b such that this function is continuous for all x.

b. Is the function differentiable at x = 3 or x = 5? Explain.

6. (10 points) Use the Intermediate Value Theorem to show there is a real root of [pic]on (1.5, 2).

7. (10 points)

a. Use the definition of derivative at a point to find the derivative of [pic] at [pic].

b. Find the equation of the tangent line to the curve at x = 2.

8. (10 points) The graph below includes the functions [pic], [pic] and [pic]. Explain which is which.

[pic]

9. (10 points) Graph a function that has the following properties:

a. [pic] b. [pic]

c. [pic] d. [pic]

e. [pic]

10. (10 points) The population P (in thousands) of Belgium from 1992 to 2000 is shown below:

|Year |1992 |1994 |1996 |1998 |2000 |

|P |10 036 |10 109 |10 152 |10 175 |10 186 |

a. Find the average rate of growth from 1994 to 1996.

b. Estimate the instantaneous rate of growth in 1996.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download