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Question

Determine the value of the constant 'k' so that function fx=kxx, if x < 0 3 ,if x 0 is continuous at x=0.

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Solution

Given, f(x)=kxx, if x<03, if x0

Since the function is continuous at x = 0, therefore,

limx0-f(x)=limx0+f(x)=f(0)limx0-kxx=limx03=3-k=3k=-3

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