Question

Evaluate limit x tends to 1 (x/x-1-1/logx)

Answer 1

Answer:

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Question

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x→1

lim

1−x+logx

x

x

−x

=

Medium

Solution

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Correct option is C)

x→1

lim

1−x+logx

x

x

−x

It is of the form

0

0

. So, applying L-Hospital's rule,

=

x→1

lim

−1+

x

1

x

x

(1+logx)−1

Again of the form

0

0

, so applying L-Hospital's rule,

x→1

lim

−

x

2

1

x

x

(1+logx)+x

x

logx(1+logx)+x

x−1

=−2