61 - Calculus Questions Answers

which of the following is differntiable at x=0 ?

cos(lxl)+lxl

sin(lxl)-lxl

Asked By: NIKHIL VARSHNEY
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Joshi sir comment

sin(|x|)+|x| is differentiable at x = 0

LHD of first = {cos|0+h|+|0+h|-cos|0|-|0|}/0+h-0  = (cosh+h-1)/h = (1-2sin2h+h-1)/h = 1 (on taking limits)

now check RHD, its value will be -1

similarly in second both values are 0 so it is differentiable

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