MATH 203 Spring 2007

TEST 1

8 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. Suppose $f$ is a piece-wise defined function:
    MATH
    (a) Sketch the graph of the function. (b) Discuss the continuity of $f$.
    MATH


  2. Compute the derivative of $h(x)=-x^{2}+3x-2$ at $a=0$ by evaluating a certain limit.
    MATH

  3. Find the derivative of MATH
    MATH

  4. What is the slope of the line tangent to the graph of the function $f(x)=2x^{2}+x+1$ at the point $(0,1)?$


  5. Evaluate the derivative of MATH
    MATH

  6. Evaluate the derivative of MATH


  7. Find the second derivative of $h(x)=2x^{\pi }.$
    MATH

  8. Find the derivative of MATH

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