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Question

limx[xx2+4x4+16]


A
4
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B
8
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C
2
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D
16
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Solution

The correct option is B 2
limx[xx2+4x4+16]
Rationalising the terms inside the bracket
=limx[xx2+4x4+16×xx2+4+x4+16xx2+4+x4+16]

=limx[x2(x2+4)(x4+16)xx2+4+x4+16]

=limx⎢ ⎢ ⎢ ⎢4x216x21+4x2+x21+16x4⎥ ⎥ ⎥ ⎥

=limx⎢ ⎢ ⎢ ⎢416x21+4x2+1+16x4⎥ ⎥ ⎥ ⎥

=41+1
=2

Mathematics

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