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Question

Let f(x)={tankxx,x<03x+2k2,x0. If f(x) is continuous at x=0, then number of values of k is

A
1
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B
2
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C
more than 2
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D
none
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Solution

The correct option is B 2
(LHL at x = 0)=limx 0 f(x)
=limh 0 f(0h)
=limh 0 tank(h)h
=limh 0 tankhkh×k=k
(RHL at x = 0)=limx 0+ f(x)
=limh 0 f(0+h)
=limh 0(3h+2k2)
=2k2
As f(x) is continuous at x=0.
(LHL at x = 0)=(RHL at x = 0)
k=2k22k2k=0k=0 or 12

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