If f(x)=(x)1x−1 for x≠1 and f is continuous at x=1 then f(1)=
A
e
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B
e−1
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C
e−2
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D
e2
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Solution
The correct option is Ae Given that the function is continuous at x= 1 ⇒limx→1f(x)=f(1) limx→1f(x)=limx→1x1/(x−1)=limx→1(1+x−1)1/(x−1)(1∞form)=elimx→1x−1x−1=e Hence f(1) is also equal to e.