If the function f defined as f(x)=1x−k−1e2x−1,x≠0 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 Cf(0)=1 f(x)=1x−k−1e2x−1,x≠0 f(x)is continuous at x=0 ⇒f(0)=limx→0(1x−k−1e2x−1) ⇒f(0)=limx→01+(2x)+12!(2x)2+⋯+(−1−x(k−1))2x2(e2x−12x)
For limit to exist the coefficient of x should be 0. ∴k=3,f(0)=1