#### MATH 1501

##### Midterm 2 - Practice | Fall '13| Barone
1. Find

2. Use the properties of natural log to simplify first, then find

3. A triangle with hypotenuse length 5, height 4 and base x is shrinking asHow fast is the area shrinking when x = 3?

4. Write the sum in sigma notation.

5. Evaluate.

6. A snowball in the shape of a sphere of radius r is melting such thatcm/hr. How fast is the volume changing when r = 3 cm?

7. Find the linearization of $\sin(x)$ at $x = 0$ and use it to approximate $\sin(0.2)$.

8. Letand note that the slope of the secant line passing through $(1, 1)$ and $(9, 3)$ is $m = 1/4$. The mean value theorem asserts that there exists a $c$ in the interval $[1, 9]$ such thatSince the function $f$ is increasing, this $c$ is unique. Find it.

9. Find and classify the critical points ofWhat is the absolute maximum and absolute minimum of $f(x)$ on the interval $[−1, 4]$?

11. Find a Riemann sum which approximates the area under the curve $y = \sin(x)$ between $x = 0$ and $x = 2π$ using $n = 6$ rectangles using left-endpoint approximation and evaluate.
12. Suppose. Find the critical points of $f$. Find the intervals where $f$ is increasing and where $f$ is decreasing, and the intervals where $f$ is concave up and concave down. Use the second derivative test to classify the critical points of $f$ as local maxima/minima or neither.