NCERT Solutions class-11 Maths Exercise 13.1

myCBSEguide App

myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

Install Now

 

Exercise 13.1

Evaluate the following limits in Exercises 1 to 22.

1.

Ans. 3 + 3 = 6


2.

Ans.


3.

Ans.


4.

Ans.


5.

Ans.


6.

Ans.

Putting as


7.

Ans.

=

=


8.

Ans.

=

=

=


9.

Ans.


10.

Ans.

=

=

=

= = 1 + 1 = 2


11.

Ans.

=

= = 1


12.

Ans. =

=

= =


13.

Ans.

=

= =


14.

Ans.

=

=

=

=


15.

Ans.

Putting as

=

= =

= =


16.

Ans. =


17.

Ans. =

= =

=

= =


18.

Ans.

=

=

=

=


19.

Ans. =

= = = 0


20.

Ans.

Dividing numerator and denominator by

=

= = = 1


21.

Ans. Given:

= =

= =

= = 0


22.

Ans. Given:

Putting as

= =

= =

=


23. Find and where

Ans. Given:

Now =

And = 3 (1 + 1) =


24. Find where

Ans. Given:

L.H.L.

Putting as

=

= = 0

R.H.L.

Putting as

=

= =


25. Evaluate where

Ans. Given:

L.H.L.

Putting as

= = =

R.H.L.

Putting as

= = =

Here, L.H.L. R.H.L.

Therefore, this limit does not exist at


26. Find where

Ans. Given:

L.H.L.

Putting as

= = =

R.H.L.

Putting as

= = =

Here, L.H.L. R.H.L.

Therefore, this limit does not exist at


27. Find where

Ans. Given:

L.H.L.

Putting as

=

= = 0

R.H.L.

Putting as

=

= = 0

Here, L.H.L. = R.H.L.

Therefore, this limit exists at and


28. Suppose and if what are possible values of and ?

Ans. Given: and

and……… (i)

Now

Putting as

= ……….(ii)

Again

Putting as

= ……….(ii)

Putting values from eq. (ii) and (iii) in eq. (i), we get

and

On solving these equation, we get and


29. Let be fixed real numbers and define a function What is ? For some compute

Ans. Given:

Now

=

= = 0

Also

=


30. If for what values of does exists?

Ans. Given:

exists for all

Now L.H.L.

Putting as

=

= = 0 + 1 = 1

Also R.H.L.

Putting as

=

= =

Here, L.H.L. R.H.L.

Therefore, this limit does not exist.


31. If the function satisfies valuate

Ans. Since


32. If for what integer and does both and exist?

Ans. Both and exist.

and

Now

= =

And

= =

……….(i)

Therefore, for exists we need

Again

= =

And

=

=

Therefore, exists for any integral value of and


http://mycbseguide.com/examin8/




5 thoughts on “NCERT Solutions class-11 Maths Exercise 13.1”

Leave a Comment