Question

Answer both and show work.

1y=fle) L-5. Given the graph of the function f(x) shown to the right-the same graph is - used for L-2. Identify any points where f(2) is not con- tinuous and explain why using precise mathematical statements in relation to how the definition of continuity is not sat- isfied. You may refer to work in L-2 rather than repeat it. L-3. Given the function g(2) defined piecewise below, determine each of the following values, showing clearly which rule was used in the calculation. Indicate if a value does not exist by writing DNE. (2x+8, 2<-2 2? +r+2, -2<<0, g(x) = 3 3-x 0<x<3, 2.0 - 5. 13 Note that this same function is used for L-6. (a) lim_9(x) = lim 9(x) = lim 9(x) = (b) lim g(x) = lim g(x) = lim g(x) =

Answer 1

Qs In Given fuction not at Graph continuous x = -3 and at a= 5 at hiltiho exist x=-3 the limit of but Raih DNE. x=5 the limit DNE. at 03. gcsop 2370 2<-2 Jeas - (x²+x+2 1 3-2 (2x-5 - < x < 0 ola <3 x 73. gca) = (a) lim de 72 lim 202-h ta hro lim 4 - 2 h ta hro l 12 A lim gra) X 7-2+ = lim (2th) ²7 (2th) 72 470 - lim 4+4 ht h²+2tht2 hyo = - DNE. lim gra) x -2

(b) lim gra) = de 3- lim3-(3-h) RYO - lim 3-3th hro = 0. = lim 2(3th) - 5 ho = lim 6+2h - 5 hro * lim gra) d3t = 1 * lim qca) – DNE 3
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