Exam 3

1. Given the graph, determine the equation

2.  Solve for all equations

${\log }_{3}x +\hspace{0.17em}{\log }_3 (x–2) = {\log }_3 (x+10)$

3.  If you invest $1,000 at an annual interest rate of 5% compounded continuously, calculate the final amount you will have in the account after five years.

4.  True or False

$\frac{d}{dx}\left(e^x\right)=e^x$

5.  Find the derivative

$y=\frac{e^{–x^3}}{2x}$

6.  Find the derivative

$f\left(x\right)=\ln (x^3–5x^2–3)$

7.  Using logarithmic differentiation find the derivative of

$f\left(x\right)={(3x–5)}^2{(2x+5)}^{–3}$

8.  Find the indefinite integral

$\int xdx$

9.  Determine the u value if using the integration by substitution method to evaluate the integral

$\int \frac{x^2+2x}{x^3+3x^2–1}dx$

10.   Given the Riemann Graph

Determine the type of Riemann and type of value.

  Left Hand Riemann and Under Score 
  Right Hand Riemann and Over Score 
  Midpoint Riemann and Under Score 
  None of the Above 

11.  Evaluate the definite integral

${\int }_1^4\frac{3x^3–2x^2+x}{x}dx$

12.  Given the graph find the area of the shaded region

13.   Given the graph 

the interval to find the area of the shaded region is 

${\int }_{–2}^2(x^3–4x^2–4x+16)dx + {\int }_2^4(x^3–4x^2–4x+16)dx$

14.  An investor is investing $3.3 million a year in an account returning 9.4% APR. Assuming a continuous income stream and continuous compounding of interest, how much will these investments be worth 10 years from now?