Question

6. (10 points) The graph of a function fis given below. O O . a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity Gump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: lim f(x) it. limf(x) ill. lim 1.

Answer 1

(a) For 2= -2,2 the function is not conti nous At 2=-2 there is removable / discontinuity At x=2 there is jump discontinuity (6) Function is not differentiable where it is not continous and where sharp are edges so, x= -2, S a=-1 Here not differentiable 2 = 0 2- 2

2 1 lim f(x) 22+ 6 - lim f(x) 2.2- then, since are they not equal defined soi kino fcx) • is not 2~2 um f(x) = 9 xt-2 cim f(x) = 9 2-7-2t lim at-2 29