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lim x tends to 0 (root[2]cosx-1)/(cotx-1) a) 0 b)1/2 c) 1 d) none of these.

lim x tends to 0    (root[2]cosx-1)/(cotx-1)


a) 0


b)1/2


c) 1


d) none of these.

Grade:11

8 Answers

ayush jain
30 Points
9 years ago

(c) 

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Arnab,

 

(√2cosx-1)/(cotx-1) = (√2cosx-1)sinx/(cosx-sinx).

 

Now this clearly tends to 0, as x tends to 0.

Hence Option (A).

 

Hope it helps.

 

Regards,

Ashwin (IIT MadraS).

Arnab Mandal
18 Points
9 years ago

Answer is 1/2.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Arnab,

 

1/2 cannot be the answer. It is wrong (must be a printing error in the source from where you got it).

You can clearly see that (√2cosx-1)sinx/(cosx-sinx), will tend to (√2-1)*0/(1-0) = 0, as x tends to 0.

 

Hence 0 is the answer my dear.

You can check the working yourself.

 

Hope it helps.

All the best.

 

Regards,

Ashwin (IIT MadraS).

Arnab Mandal
18 Points
9 years ago

using L Hospital rule its coming 1/2.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Arnab,

 

You should be careful while applying L-Hospital Rule.

 

It is applicable on limtis of the form (0/0) or (∞/∞).

This limit is not of that form.

Hence L-Hospital Rule cannot be applied to this limit.

 

Best Regards,

Ashwin (IIT MadraS).

Arnab Mandal
18 Points
9 years ago

extremely sorry , x tends to pi/4, not zero.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Arnab,

 

Never mind.

In that case, you apply L-Hospital rule and get the answer.

But yeah, the question could be x tending to 0 as well. In which case it is 0.

 

All the best.

 

Regards,

Ashwin (IIT Madras).

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