MATH 203 Spring 2009

TEST 3

7 problems, 10 points each

Instructions:

Show enough work to justify your answers

  1. Evaluate MATH
    MATH

  2. Complete the following:
    MATH

  3. Find the antiderivative $F$ of the function $f(x)=e^{x}+x$ satisfying the initial condition $F(0)=1.$

  4. Simplify the function and then evaluate the integral MATH
    MATH

  5. Provide the formula of the Riemann sum (don't evaluate it) for the integral MATH, where function $f(x)\ $is plotted below, with $n=4$ intervals$,$ and with the left ends chosen as the sample points$.$ Provide an illustration below of the terms of the Riemann sum. What does the Riemann sum approximate?
    MATH
    $.$

  6. Find the area under the graph of the function $f(x)=e^{x}$ from $x=-1$ to $x=1.$
    MATH

  7. Find the average value of the function $f(x)=2x^{2}-3$ on the interval $[1,3]$.

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