MATH 203 Spring 2007

FINAL EXAM

11 problems, 10 points each

Instructions:

1. Show enough work to justify your answers

2. Write the problems in the given order.

3. Don't leave blank pages.

  1. Compute the derivative of $h(x)=3x^{2}-3x$ at $a=1$ by evaluating a certain limit.
    MATH

  2. Evaluate the derivative of MATH Find an equation of the line tangent line to the graph of the function at the point $(0,0)?$
    MATH

  3. Find the second derivative of $h(x)=xe^{x}.$

  4. Find the derivative of MATH
    MATH

  5. The graph of function $f$ is given below. Sketch the graph of the derivative $f^{\prime }(x)$ in the space under the graph of $f$.

    MATH.

  6. Find absolute (global) maxima and minima of the function, $f(x)=x^{3}-3x$ on the interval $[-2,10].$
    MATH

  7. Evaluate the integral: MATH
    MATH

  8. Evaluate the integral by substitution $\int xe^{x^{2}}dx.$

  9. Find the area of the region bounded by $y=x^{2}-1$ and $y=3.$
    MATH

  10. Computer the partial derivatives of MATH

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