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Discuss the differentiability of`f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a tx=0` |
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Answer» LHD=`lim_(x->0^-) (xe - (-1/x + 1/x) - 0)/(x-0) ` `= lim_(x->0^-) (xe)/x = e` RHD= `lim_(x->0^+) (xe- (1/x + 1/x) - 0)/(x-0)` `= lim_(x->0^+) (xe- 2/x)/x` `= lim_(x->0^+) (x^2e-2)/(x^2) = (0-2)/0 = -oo` LHD=`e` RHD=`-oo` LHD`!=`RHD `:.` f(x) is not differentiable Answer |
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