## Problem 1-4 (5 pts. each)

1. Consider the following integral:

a. The integral is indefinite.
b. The integral is proper.
c. The integral is improper because the interval of integration is not bounded.
d. The integral is improper because the integrand has vertical asymptotes inside or at the bounds of interval of integration.

2. Which of the following polynomials is a Taylor approximation at $x = 0$ for the function $f(x) =sinx$ ?
Circle the correct answer (there is only one).
a.
b.
c.
d.
e.
f. None of these

3. Consider the rational function

When writing out the partial fraction expansion of this rational function, the first step is to set it equal to which of the following expressions (all Greek letters below are treated as unknown):
a.
b.
c.
d. None of these.

4. A scientist is measuring the weight of fa hippo over a period of months. She uses the function $w(t)$ to represent the weight of the hippo $t$ months after the experiment has begun. What does the integral

represent?
a. The average weight of the hippo during the period [2,5]
b. The weight of the hippo 5 months after the experiment began + the weight of the hippo 2 months after the experiment began.
c. the cumulative change in the hippo’s weight over the period [2, 5]
d. The area under the hippo.
e. None of these.

a.
b.
c.
d.

## Problem 6

Let $G(x)$ be the function defined by

Evaluate the derivative $G’(x)$. (Put a box around your final answer.)

## Problem 7

a. Evaluate the following integral: