# NCERT Solutions Class 11 Mathematics Chapter 13 Limit and Derivatives Miscellaneous Solutions

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## Formulas and Definitions Chapter 13 Class 11 Maths Limit And Derivatives Ncert Solutions

What is limit in mathematics limit x tends to 2 (x^2 -4)/ x - 2 , form of 0 by 0

## Exercise Solutions 13.1 Chapter 13 Class 11 Maths Limit And Derivatives Ncert Solutions

Example 1 : Limit x tends to 3 (x^3 - 27)/(x- 3) and Limit x tends to -2(x^3 + 8)/(x^2- 4)

Example 2 : lim x tends to 2 (x^2 + 3x - 10)/(x^2 + 5x - 14)

Example 3 :limit x tends to -3 (x^4 - 81)/ (x^2 - 9) and limit x tends to -3 (x^4 - 81)/ (x + 3)

Example 4 : limit x tends to 3 (x^5 - 243)/( x-3) , - 2 (x^7 + 128)/(x+ 2) use of formula (x^n - a^n) /( x - a)

Example 5 : limit x tends to -3 (x^4 - 81) /(x^5 + 243)

Exercises Solutions 1-12
1 - 7 Evaluate the following limits in lim x tends to 0 {(x + 1)^5 -1} /x

8-10 Ncert solution of chapter 13 question 8 to 10

11-12 limit x → - 2 (1/x + 1/ 2)/(x+ 2) evaluate the limit

Important Question of limits for home work

Home work answer check ncert solution for class 11 chapter 13 limits with solution

Explanation of Home work Questions:
limit x → -3 (x^2 - x- 12) / (x^2 - 9), x → -2 (x^8 - 256) / (x+ 2), x → 2 (x^5 - 32) /( x^7 - 128)

Explanation of Home work Questions:
limits and derivatives class 11 limit x tends to - 3 (x ^2 - 9) / (x + 3)

Exercise Question 13- 14
Introduction to limit for trigonometric Functions

Example 6 : limit x - zero {sin^2 ax / (tan bx tan cx)} limits of trigonometric functions

Example 7 : limits of trignometric functions limit x tends to 0 (1 - cos ^4 x) / x^2

Example 8 : Evaluate limit x tends to 0 (1 - cos 3x) /sin 2x sin 3x

Example 9 : Evaluate limit x tends to 0 (1 - cos mx)/(1- cos nx)

Example 10 : Evaluate limit x tends to pi tanx /(x - pi)

Example 11 :limits and derivatives class 11 ncert solution Evaluate limit x tends to pi sin x / x - pi

Example 12 :limit x tends to pi/2 (2x - pi)/cosx

Example 13 :limit x tends to pi/2 (1 + cos 2x)/(pi - 2x)^2

Exercise Question 15 - 17
limit x → pi sin (pi - x)/ pi (pi-x) , lim →0 cos x / pi - x , lim x → 0 cos 2x - 1 / cos x -1

18. limit x tends to zero (ax + xcosx) divide by bsinx

19- 20 : limit x tends 0 xsecx , lim x tends to zero (sinax + bx)/(ax + sinbx)

21 limit x tends to 0 (cosec x - cotx)

22. limit x tends to pi/2 tan2x /(x- pi/2)