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Question

If fx=2x2+k,if x0-2x2+k,if x<0, then what should be the value of
k so that f(x) is continuous at x = 0.

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Solution

The given function can be rewritten as

fx=2x2+k, if x0-2x2+k, if x<0

We have
(LHL at x = 0) = limx0-fx=limh0f0-h=limh0f-h=limh0-2-h2+k=k

(RHL at x = 0) = limx0+fx=limh0f0+h=limh0fh=limh02h2+k=k

If fx is continuous at x=0, then

limx0-fx =limx0+fx = f0limx0-fx =limx0+fx = k

∴ k can be any real number.


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