Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = x4 − 2x2 + 1, a = 2 ∞ f n(2) n! (x − 2)n n = 0 = 24 + 9(x − 2) + 22(x − 2)2 + 8(x − 2)3 + (x − 2)4 ∞ f n(2) n! (x − 2)n n = 0 = −9 + 24(x − 2) + 22(x − 2)2 + 8(x − 2)3 + (x − 2)4 ∞ f n(2) n! (x − 2)n n = 0 = 24 + 9(x − 2) + 8(x − 2)2 + 22(x − 2)3 + (x − 2)4 ∞ f n(2) n! (x − 2)n n = 0 = 9 + 24(x − 2) + 22(x − 2)2 + 8(x − 2)3 + (x − 2)4 ∞ f n(2) n! (x − 2)n n = 0 = 9 + 24(x − 2) + 8(x − 2)2 + 22(x − 2)3 + (x − 2)4

Question 13 of 451 pointwhich statement correctly describes the inverse of the following function? a. it is negative. b. it is a horizontal shift. c. it is not a function. d. it is a function. give an explanation as to why you chose that answer. (i think its either a or d.)

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.