show that ` f(x)=x^(3)` is contiuous at x=2 – InterviewSolution

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1.	show that ` f(x)=x^(3)` is contiuous at x=2
Answer» we have `f(2) =2^(3)=8` `lim_(xto2+)f(x) = lim_(hto0)(2+h)^(3) =lim_(hto0) (8+h^(3) +12h +6h^(2))=8,` ` lim_(x to 2-) f(x) = lim_(hto0) (2 -h)^(3) = lim_(h to 0) ( 8-h^(3) -12h +6h^(2)) =8 ` `lim_(x to 2x) f(x) = lim_(x to 2-) f(x) = f(2)` Hence , f(x) is continous at x =2 .

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