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Question

The value of limx0(tanx7+cos3x7)14/x is

A
e1
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B
e2
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C
1
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D
e
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Solution

The correct option is B e2
L=limx0(tanx7+cos3x7)14/x (1 form)

=exp{limx014x(tanx7+cos3x71)}=exp⎪ ⎪ ⎪⎪ ⎪ ⎪2limx0⎜ ⎜ ⎜tanx7x7+3⎜ ⎜ ⎜cos3x713x7⎟ ⎟ ⎟⎟ ⎟ ⎟⎪ ⎪ ⎪⎪ ⎪ ⎪

=exp⎪ ⎪ ⎪⎪ ⎪ ⎪2limx0⎜ ⎜ ⎜tanx7x73⎜ ⎜ ⎜2sin23x143x7⎟ ⎟ ⎟⎟ ⎟ ⎟⎪ ⎪ ⎪⎪ ⎪ ⎪

=exp⎪ ⎪ ⎪⎪ ⎪ ⎪2limx0⎜ ⎜ ⎜tanx7x73⎜ ⎜ ⎜2sin3x143x142sin3x14⎟ ⎟ ⎟⎟ ⎟ ⎟⎪ ⎪ ⎪⎪ ⎪ ⎪

=exp(2(10))
=e2

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