TEST 1



To receive credit, you must show a sufficient amount of work in deriving your solution. Total 50 points.

1. Test the convergence of the following sequence:

a) [pic]

b) [pic]

2. Find a formula for the general term of [pic]

3. Find the sum of the convergent harmonic series [pic]

4. Determine the values of x for which the series [pic]converges

5. Determine whether the series is absolutely convergent, conditionally convergent,

or divergent

a) [pic]

b) [pic]

6. Find the radius of convergence and interval of convergence of series [pic].

7. Find a power series representation of the function and determine interval of convergence

a) [pic]

b) [pic]

8. Find the Maclaurin series of [pic]

9. Integrate by power series representation: [pic]

10. Eliminate the parameter to find a Cartesian representation of [pic]. Also sketch the curve.

Bonus question: Write the calculator code to draw the following HAPPY FACE: the mouth is the semicircle

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