Using Series to Evaluate Limits and Integrals Worksheet with Answer Key

What's on the worksheet

1. Find each limit by writing the top and the bottom as series near 0 and keeping the lowest power that survives.
   \displaystyle\lim_{x \to 0} \dfrac{e^x - e^{-x} - 2x}{x^3}\displaystyle\lim_{x \to 0} \dfrac{\arctan x - \sin x}{x^3}\displaystyle\lim_{x \to 0} \dfrac{\cos x - e^{-x^2/2}}{x^4}\displaystyle\lim_{x \to 0} \dfrac{e^x - 1 - x}{x - \arctan x}
2. The integral I = _0^0.74 (x³)\,dx has no antiderivative built from the familiar functions.
3. Let $g
4. Let $F
5. Let $f
6. Let $f