Question

please do problems a-c, thank you

1.7 Preview Activity: Limits, Continuity, and Differentiability A function f defined on the interval 4 < x < 4 is given by the graph shown here. Use the graph to answer the questions. a. For each of the values a = -4,-3, -2,-1,0, 1, 2, 3, determine whether or not limf(x) exists. If the function has a limit Lat a given point, state the value of the limit using the notation limf(x) L. If the function does not have a limitata given point, write a sentence to explain why. b. For each of the values of a from part (a) where f has a limit, determine the value of (a) at each such point. In addition, for each such a value, does f(a) have the same value as limf(x)? C. For each of the values q = -4,-3, -2,-1,0, 1, 2, 3, determine whether or not f'(a)exists. In particular, based on the graph, ask yourself if it is reasonable to say that f has a tangent line at (0./(@)) for each of the given a-values. If so, visually estimate the slope of the tangent line to approximate the value of f'(a).

Answer 1

lim fen) = lim feasso, lim fex) limeni him forse -4 97-47 thing tº lim fex) = 3, lim_ fex)=2 , im feas a lima tas xy-gt イラー lim tea)zo lim franzo0 lim flas- lim feas = 1 anot lim kasa limfn) = 2, lim flas a lim fix) ny37 lim fix a limeter feras. Since left and right limit of feas at o anda are not equal. so, limit of fears at o and a are not exists. f1.4) ao not given. &(-3) = 2, f(-2) = 2 +(-1)= lim fem), lim fta) = f(1) = 1, dim fex) = 2 2 f1z), lim fena f(3) lim flugfeng & naio

I (2) is not exists be cause fort has a two tangent at x 22 de