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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