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

Question 1:

Find the limits :

Question 2:

Find the limits :

Question 3:

Find the limits :

Question 4:

Find the limits :

Question 5:

Find the limits :

Question 6:

Find the limits :

Question 7:

Find the limits :

Question 8:

Find the limits :

Question 9:

Evaluate :

Question 10:

Evaluate :

Question 11:

Evaluate :

Question 12:

Evaluate :

Question 13:

Find the derivative at x = 2 of the function f(x) = 3x.

Question 14:

Question 15:

Find the derivative of sin x at x = 0.

Question 16:

Find the derivative of f (x) = 3 at x = 0 and x = 3.

Question 17:

Find the derivative of f (x) = 10x.

Question 18:

Question 19:

Find the derivative of the constant function f (x) = a for a fixed real number a.

Question 20:

Question 21:

Question 22:

Question 23:

Question 24:

Question 25:

Find the derivative of ‘f’ from the first principle, where ‘f’ is given by :

Question 26:

Find the derivative of ‘f’ from the first principle, where ‘f’ is given by :

Question 27:

Find the derivative of f (x) from the first principle, where f (x) is :
sin x + cos x

Question 28:

Find the derivative of f (x) from the first principle, where f (x) is :
x sin x

Question 29:

Compute the derivative of :
f (x) = sin 2 x

Question 30:

Find the derivative of :

Question 31:

Find the derivative of :

Question 32:

Evaluate the following limits:

Question 33:

Evaluate the following limits:

Question 34:

Evaluate the following limits:

Question 35:

Evaluate the following limits:

Question 36:

Evaluate the following limits:

Question 37:

Evaluate the following limits:

Question 38:

Evaluate the following limits:

Question 39:

Evaluate the following limits:

Question 40:

Evaluate the following limits:

Question 41:

Evaluate the following limits:

Question 42:

Evaluate the following limits:

Question 43:

Evaluate the following limits:

Question 44:

Evaluate the following limits:

Question 45:

Evaluate the following limits:

Question 46:

Evaluate the following limits:

Question 47:

Evaluate the following limits:

Question 48:

Evaluate the following limits:

Question 49:

Evaluate the following limits:

Question 50:

Evaluate the following limits:

Question 51:

Evaluate the following limits:

Question 52:

Evaluate the following limits:

Question 53:

Evaluate the following limits:

Question 54:

Question 55:

Question 56:

Question 57:

Question 58:

Question 59:

Question 60:

Question 61:

Question 62:

Question 63:

Question 64:

Find the derivative of x² – 2 at x = 10.

Question 65:

Find the derivative of 99x at x = 100.

Question 66:

Find the derivative of x at x = 1.

Question 67:

Find the derivative of the following functions from first principle :
x³ – 27

Question 68:

Find the derivative of the following functions from first principle :
(x – 1) (x – 2)

Question 69:

Find the derivative of the following functions from first principle :

Question 70:

Find the derivative of the following functions from first principle :

Question 71:

Question 72:

Question 73:

For some constants a and b, find the derivative of :
(x – a) (x – b)

Question 74:

For some constants a and b, find the derivative of :
(ax² + b)²

Question 75:

For some constants a and b, find the derivative of :
(x – a) (x – b)

Question 76:

Question 77:

Find the derivative of :

Question 78:

Find the derivative of :

Question 79:

Find the derivative of :

Question 80:

Find the derivative of :

Question 81:

Find the derivative of :

Question 82:

Find the derivative of :

Question 83:

Find the derivative of cos x from first principle.

Question 84:

Find the derivatives of the following functions :
sin x cos x

Question 85:

Find the derivatives of the following functions :
sec x

Question 86:

Find the derivatives of the following functions :
5 sec x + 4 cos x

Question 87:

Find the derivatives of the following functions :
cosec x

Question 88:

Find the derivatives of the following functions :
3 cot x + 5 cosec x

Question 89:

Find the derivatives of the following functions :
5 sinx – 6 cos x + 7

Question 90:

Find the derivatives of the following functions :
2 tan x – 7 sec x