InterviewSolution
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InterviewSolution
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The value of k for which `f(x)={{:(,[1+x(e^(-1//x^(2)))sin(1/(x^(4)))]^(e1//x^(2)),x ne 0),(,k,x=0):}` is continuous at x=0, isA. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - A For f(x) to be continuous at x=0, we must have `underset(x to 0)lim f(x)=f(0)` `Rightarrow underset(x to 0)lim (1+xe^(-1//x^(2))"sin"(1)/(x^(4)))^(e^(1//x^(2)))=k` `Rightarrow underset(e^(x) to 0)lim (x" "e^(1//x^(2)) e^(1//x^(2)) "sin"(1)/(x^(4)))=k` `Rightarrow underset(e^(x) to 0)lim x "sin"(1)/(x^(4))=k` `Rightarrow e^(0)=k Rightarrow k=1` |
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