Find the taylor series about 0 for each of the functions below. give the first three non-zero terms for each.

a. x2sin(x2)−x4= + + +⋯

b. 2cos(x)+x2= + + +⋯ for each of these series, also be sure that you can find the general term in the series!

Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?