State the following. The Alternating Series Test

The graph of $f$ is given. Use it to graph the function $y=-f(-x)$.

State the following. The Limit Comparison Test

A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0<r<1. Suppose that the ball is dropped from an initial height of H meters. Assuming that the ball continues to bounce indefinitely, find the total distance that it travels.

State the following. The Comparison Test

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function. $y=e^{x} \ln (1-x)$

Use the partial fraction command on your CAS to find a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum the series directly.

$$^∞∑ n=1 3n^2+3n+1/(n^2+n)^3$$

State The Direct Comparison Test.

To construct the snowflake curve, start with an equilateral triangle with sides of length 1. Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle on the middle part, and then delete the middle part. Step 2 is to repeat step 1 for each side of the resulting polygon. This process is repeated at each succeeding step. The snowflake curve is the curve that results from repeating this process indefinitely. Sum an infinite series to find the area enclosed by the snowflake curve.

State the following. The Integral Test

The graph of $f$ is given. Use it to graph the function $y=f(-x)$.

To construct the snowflake curve, start with an equilateral triangle with sides of length 1. Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle on the middle part, and then delete the middle part. Step 2 is to repeat step 1 for each side of the resulting polygon. This process is repeated at each succeeding step. The snowflake curve is the curve that results from repeating this process indefinitely. Show that $p_{n} \rightarrow \infty \text { as } n \rightarrow \infty$.

Determine whether the series converges or diverges. summation from n=1 to infinity 9^n/3+10^n

State the following. The Test for Divergence