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Show that the function `f(x)=2x-|x|`is continuous but notdifferentiable at `x=0` |
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Answer» `f(x)=2x-x,x>=0` `f(x)=2x-(-x),x<0` f(x) is continuous when lim f(x)=limf(x)=f(0) `LHL=lim_(x->0^-)(3x)=0` `RHL=lim_(x->0^+)=0` `f(0)=0` f(x) is differential only when LHD=RHD `LHD=lim_(x->o^-)(f(x)-f(0))/(x-0)=lim_(x->0^-)((3x-0)/(x-0))=3` `RHD=lim_(x->0^+)((f(x)-f(0))/(x-0))=lim_(x->0^+)((x-0)/(x-0))=1` `LHD!=RHD` f(x) is not differential at x=0. |
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