InterviewSolution
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InterviewSolution
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Show that the function `f(x)=2x-|x|`is continuous at `x=0`. |
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Answer» we have, ` f(0) =(2xx 0) -|0|=0` `lim_( x to 0+) f(x) = lim_(h to 0) f( 0+h) ` ` lim_(h to 0) ( 2h-|h|) = lim_( h to 0) ( 2h-h) = lim_( h to 0) h =0` ` lim_(x to 0-) f(x) - lim_(hto0) f( 0-h)` `lim_(hto0) {2(-h)-|-h|}=lim_(hto0)(-2h-h) = lim_(hto0) (-3h) =0` Thus, ` lim_(xto0+) f(x) = lim_(xto0+) f(x)=0and " therefore " , lim_(xto0) f(x)=0` ` lim_(x to 0) f(x) = f(0) =0` Hence, f(x) is continuous at x =0 |
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