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Question

limy 0 1+1+y4 2y4

A
does not exist
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B
exists and equals 122
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C
exists and equals 142
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D
exists and equals 122 (2+1)
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Solution

The correct option is C exists and equals 142
limy 0 1+1+y4 2y4
Now rationalizing the numerator, we get
limy 0 1 + 1+y4 2y4×11 + 1+y4 + 2

=limy 0 1 + 1+y4 2y4×122

=limy 0 1+y4 1y4×122
=122×limy 0 4y321+y44y3
[Using L Hopital rule]

=122×12=142


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