Question

6. (10 points) The graph of a function fis given below. 2 a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity (jump, 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: i. lim f(x) ii. limf(x) ill. lim f(x) 22+

Answer 1

xt-2 According to the graph of t. f(x). y f(x) is not continuous at x-F2,2] (ans) in the interval (-4,4). X=-2 is a removeable discontinuity since, lim f(x) + f(-2) x=2 is a Jump dis continuity since, lim f(x) & lim f(2). & f(2). x42t 6) *= f(x) is not continuous at X=-2, 2. So, f(x) is not differentiable at =-2,2. Also, fex) has sharp edge at x=1. So, fex) is not differentiable at u=-1. fou is not differentiable at at 241-2,2 in (-4,4) x+2- Ans) et2 . C) lim f(x) = 12 (Ans U X+21 lim f(x)=2, lim f(x)=8 10) 2727 lim fex) & lim lim f(x) X+21 2+2 So, lim f(x) 2+2 lim fowla9 [ X+-2 lim f(x) = 9 X+-24 does not exists. (445) iii) lim f(x) = [9. Ans) X+-2