022 Exam 2 Sample A

This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

Find the derivative of  $y\,=\,\ln {\frac {(x+5)(x-1)}{x}}.$

 Problem 2 

Find the antiderivative of  $y\,=\,3x^{2}-12x+8.$

 Problem 3 

Find the antiderivative of $\int {\frac {1}{3x+2}}\,dx.$

 Problem 4 

Find the antiderivative of $\int (3x+2)^{4}\,dx.$

 Problem 5 

Set up the equation to solve. You only need to plug in the numbers - not solve for particular values!

How much money would I have after 6 years if I invested $3000 in a bank account that paid 4.5% interest,

(a) compounded monthly?

(b) compounded continuously?

 Problem 6 

Find the area under the curve of  $y\,=\,{\frac {8}{\sqrt {x}}}$  between $x=1$ and $x=4$.

 Problem 7 

Find the quantity that produces maximum profit, given the demand function $p\,=\,90-3x$ and cost function $C\,=\,200-30x+x^{2}$.