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Evaluate the following limit: lim x→1 [(1+x)/(2+x)] [(1-√x)/(1-x)]

Evaluate the following limit:


lim x→1  [(1+x)/(2+x)][(1-√x)/(1-x)]

Grade:12th Pass

3 Answers

suchita undare
20 Points
9 years ago

(1-√x)/(1-x) = (1-√x)(1+√x)/(1-x)(1+√x)=(1-x)/(1-x)(1+√x)=1/(1+√x)

put this rationalised value in expression

lim x→1 [(1+x)/(2+x)][1/(1+√x)]

since this expression does take any indeterminant form put x=1

=(2/3)1/2

hope this works...

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Menka,

 

The following limit can be written as (2/3)lim x→1 (1-√x)/(1-x) , that is because (1+x)/(2+x) is continuous at x=1.

 

Now the limit is lim x→1 (1-√x)/[(1-√x)(1+√x)],

Which is  lim x→1 [1/ (1+√x)]

which is 1/2.

 

Hence the limiting value is (2/3)1/2.

 

 

The solutions to your other questions on functions is ready.

Have to scan it and post it here, as there were some graphs to be made on that.

 

Will post the scanned copies soon.

 

All the best.

 

Regards,

Ashwin (IIT Madras).


SREEDHAR P
15 Points
9 years ago

lim x->1 (1+x).(1-x^1/2)/(2+x).(1-x)

rationalising with 1+x^1/2

(1+x)/(2+x).(1+x^1/2)

lim x->1 2/6 =1/3

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