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Question

The function f:(R0) R given by f(x)=1x2e2x1 can be made continuous at x=0 by defining f(0) as

A
2
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B
1
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C
0
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D
1
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Solution

The correct option is D 1
Givenf(x)=1x2e2x1
f(0)=limx0{1x2e2x1}=limx0e2x12xx(e2x1) .......[00form]
usingL'Hospital rule
f(0)=limx02e2x2(e2x1+2xe2x)
f(0)=limx04e2x4xe2x+2e2x+2e2x=4.e04(0+e0)=1

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