The derivation in example 6.6.1 shows the taylor series for arctan(x) is valid for all x ∈ (−1,1). notice, however, that the series also converges when x = 1. assuming that arctan(x) is continuous, explain why the value of the series at x = 1 must necessarily be arctan(1). what interesting identity do we get in this case?

Question 1(multiple choice worth 1 points)(07.06 mc)a group of students must collect at least $150 to organize a science fair. they have already collected $30. which graph best represents all remaining amounts of money, in dollars, that thestudents should still collect to organize the science fair? -210 -180 -150 - 120 -90-60 -300306090 120 150 180 210-210 -180 -150 - 120 -90 -60 -30 0 30 60 90 120 150 180 210-210 -180-150 - 120 -90-60-300 30 60 90 120 150 180 210-210 -180 -150 - 120.90 -60 -30 0 30 60 90 120 150 180 210

Suppose a pendulum is l meters long. the time,t,in seconds that it tales to swing back and forth once is given by t=2.01

Solve this and show you’re work step by step ! -5 3/4+3h< 9 1/4 -