Solution of Chapter 13. limits and derivatives (NCERT - Maths Book)

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Evaluate the following limits in Exercises.

Find and , where

Find , where

Evaluate , where f(x) =

Find, where

Find , where

Suppose

and if = f (1) what are possible values of a and b?

Let a₁, a₂,… , a_n be fixed real numbers and define a function

f (x) = ( x − a₁) ( x − a₂)...( x − a_n) .

What is ? For some compute .

If For what value (s) of a does exists?

If the function f(x) satisfies , evaluate

If For what integers m and n does both and exist?

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

Find the derivative of 99x at x = l00.

Find the derivative of x at x = 1.

Find the derivative of the following functions from first principle.

x³ – 27

Find the derivative of the following functions from first principle.

(x −1) (x − 2)

Find the derivative of the following functions from first principle.

Find the derivative of the following functions from first principle.

For the function .Prove that f’ (1) =100 f’ (0).

Find the derivative of for some fixed real number a.

For some constants a and b, find the derivative of

(x − a) (x − b)

For some constants a and b, find the derivative of

For some constants a and b, find the derivative of

Find the derivative of for some constant a.

Find the derivative of

Find the derivative of

Find the derivative of

Find the derivative of

Find the derivative of

Find the derivative of

Find the derivative of cos x from first principle.

Find the derivative of the following functions:

sin x cos x

Find the derivative of the following functions:

sec x

Find the derivative of the following functions:

5sec x + 4cos x

Find the derivative of the following functions:

cosec x

Find the derivative of the following functions:

3 cot x + 5 cosec x

Find the derivative of the following functions:

5 sin x – 6 cos x + 7

Find the derivative of the following functions:

2tan x – 7sec x

Find the derivative of the following functions from first principle:

–x

Find the derivative of the following functions from first principle:

(-x)^-1

Find the derivative of the following functions from first principle:

sin (x + 1)

Find the derivative of the following functions from first principle:

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x + a)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(ax + b)ⁿ

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

sin (x+a)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

cosec x cot x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):