MATH 203 Spring 2009

FINAL EXAM

10 problems, 10 points each

Instructions:

Show enough work to justify your answers

  1. Suppose you have a function $h(x)=x^{2}-1.$ Evaluate this limit:
    MATH
    What is it that you've found?
    MATH

  2. Evaluate the derivative of $f(x)=x^{2}e^{x}.$
    MATH

  3. Find the derivative of MATH


  4. Find the second derivative of $h(x)=x^{2}+x+1.$ What does it tell you about the shape of the graph of $f?$
    MATH

  5. The graph of a function $f(x)$ is given below. Estimate the values of the derivative $f^{\prime }(x)$ for $x=2,4,$ and $7.$
    final09__14.png

    MATH


  6. The graph of $f$ is given below. Describe the behavior of the function using: "increasing/decreasing on interval..", "concave up/down on interval..", "max/min at..", "asymptotes are..", etc.
    MATH

    MATH

  7. Evaluate the integral: MATH
    MATH


  8. Find the area of the region bounded by $y=\sqrt{x},$ the $x$-axis, and the lines $x=1$ and $x=4.$
    MATH

  9. Draw a few level curves of the function $f(x,y)=x^{2}+y.$
    MATH

  10. Find all critical points of the function MATH

This document created by Scientific WorkPlace 4.1.