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Question

If the function f defined as f(x)=1xk1e2x1,x0 is continuous at x=0, then

A
k=3
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B
k=1
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C
f(0)=1
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D
f(0)=3
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Solution

The correct option is C f(0)=1
f(x)=1xk1e2x1,x0
f(x) is continuous at x=0
f(0)=limx0(1xk1e2x1)
f(0)=limx01+(2x)+12!(2x)2++(1x(k1))2x2(e2x12x)
For limit to exist the coefficient of x should be 0.
k=3,f(0)=1

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