NCERT Solutions for Class 11 Maths chapter-13 Limits and Derivatives Exercise 13.2

NCERT Solutions for Class 11 Maths chapter-13 Limits and Derivatives Exercise 13.2

NCERT Solutions for Class-11 Maths Chapter-13 Limits and Derivatives

NCERT Solutions for Class 11 Maths Chapter-13 Limits and Derivatives Exercise 13.2 is prepared by rhe expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download and share NCERT Solutions for Class 11 Maths.

NCERT Solutions for Class-11 Maths Exercise 13.2

Evaluate the following limits in Exercises 1 to 22.

Question 1. Find the derivative of x ² – 2 at x = 10.

Solution :
Here f(x) = x ² – 2

Question 2.Find the derivative of 99x at x = 100.

Solution :

Let f (x) = x

Then,

Question 3. Find the derivative of x at x=1.

Solution :

Let f (x) = 99x,

From first principle

Question 4. Find the derivatives of the following functions from first principle:

(i) x ³ −27

(ii) (x−1)(x−2)

(iii)1/x ²

( iv )x+1/x−1

Solution :
(i)Let f (x) = x ³ – 27

From first principle

(ii) Let f (x) = (x – 1) (x – 2)

From first principle

(iii)Let f (x) = 1 / x ²

From first principle, we get

(iv)Let f (x) = x + 1 / x – 1

From first principle, we get

Question 5. For the function prove that f’ (1) =100 f’ (0).

Solution :

Question 6. Find the derivative of x ⁿ + ax ⁿ⁻¹ + a ² x ⁿ⁻² + …+a ⁿ⁻¹ x + a ⁿ for some fixed real number a.

Solution :

Question 7. For some constants a and b find the derivative of:

(i) (x − a) (x − b)

(ii) (ax ² + b) ²

(iii) x – a / x – b

Solution :
(i) Given:(x − a) (x − b)

(ii)(ax ² + b) ²

(iii) x – a / x – b

Question 8. Find the derivative of for some constant a.

Solution :

Question 9. Find the derivative of

(i) 2x−3/4

(ii) (5x ³ +3x−1)(x−1)

(iii) x−3(5+3x)

(iv) x ⁵ (3−6x−9)

(iv) x−4(3−4x−5)

(vi) 2/x+1 − x ² /3x−1

Solution :
(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 10. Find the derivative of cos x from first principle.

Solution :
,

Question 11. Find the derivative of the following functions:

(i) sin x cos x

(ii) sec x

(iii) 5sec x + 4cos x

(iv) cosec x

(v) 3cot + 5cosec x

(vi) 5sin - 6cos x + 7

(vii) 2tan x - 7sec x

Solution :
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)