Designed by subject matter experts, **free NCERT
Solutions** are available at Aasoka for the students of Class 11.
These solutions are drafted as per the latest CBSE syllabus in a simple and
easy-to-understand language. Students can take the help of **NCERT Solutions for
Class 11** to begin their preparations for school as well as
competitive exams. They can get an understanding of the exam pattern and type of
questions that will appear in the exams.

**“Limits and Derivatives”** chapter of Class 11 Maths discusses
derivatives of polynomials, intuitive idea of limit, the derivative of the sum,
derivatives of trigonometric functions; difference, product, and quotient of
functions;
definition of the derivative, etc.

##### Question 1:

Find the limits :

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##### Question 2:

Find the limits :

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##### Question 3:

Find the limits :

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##### Question 4:

Find the limits :

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##### Question 5:

Find the limits :

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##### Question 6:

Find the limits :

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##### Question 7:

Find the limits :

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##### Question 8:

Find the limits :

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##### Question 9:

Evaluate :

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##### Question 10:

Evaluate :

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##### Question 11:

Evaluate :

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##### Question 12:

Evaluate :

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##### Question 13:

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

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##### Question 14:

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##### Question 15:

Find the derivative of sin x at x = 0.

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##### Question 16:

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

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##### Question 17:

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

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##### Question 19:

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

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##### Question 25:

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

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##### Question 26:

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

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##### Question 27:

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

sin x + cos x

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##### Question 28:

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

x sin x

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##### Question 29:

Compute the derivative of :

f (x) = sin 2 x

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##### Question 30:

Find the derivative of :

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##### Question 31:

Find the derivative of :

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##### Question 32:

Evaluate the following limits:

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##### Question 33:

Evaluate the following limits:

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##### Question 34:

Evaluate the following limits:

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##### Question 35:

Evaluate the following limits:

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##### Question 36:

Evaluate the following limits:

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##### Question 37:

Evaluate the following limits:

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##### Question 38:

Evaluate the following limits:

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##### Question 39:

Evaluate the following limits:

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##### Question 40:

Evaluate the following limits:

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##### Question 41:

Evaluate the following limits:

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##### Question 42:

Evaluate the following limits:

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##### Question 43:

Evaluate the following limits:

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##### Question 44:

Evaluate the following limits:

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##### Question 45:

Evaluate the following limits:

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##### Question 46:

Evaluate the following limits:

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##### Question 47:

Evaluate the following limits:

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##### Question 48:

Evaluate the following limits:

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##### Question 49:

Evaluate the following limits:

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##### Question 50:

Evaluate the following limits:

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##### Question 51:

Evaluate the following limits:

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##### Question 52:

Evaluate the following limits:

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##### Question 53:

Evaluate the following limits:

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##### Question 62:

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##### Question 63:

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##### Question 64:

Find the derivative of x^{2} – 2 at x = 10.

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##### Question 65:

Find the derivative of 99x at x = 100.

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##### Question 66:

Find the derivative of x at x = 1.

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##### Question 67:

Find the derivative of the following functions from first
principle :

x^{3} – 27

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##### Question 68:

Find the derivative of the following functions from first
principle :

(x – 1) (x – 2)

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##### Question 69:

Find the derivative of the following functions from first principle :

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##### Question 70:

Find the derivative of the following functions from first principle :

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##### Question 71:

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##### Question 72:

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##### Question 73:

For some constants a and b, find the derivative of :

(x – a) (x – b)

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= (x – a) (1 – 0) + (x – b) (1 – 0)

= x – a + x – b = 2x – a – b.

##### Question 74:

For some constants a and b, find the derivative of :

(ax^{2} + b)^{2}

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##### Question 75:

For some constants a and b, find the derivative of :

(x – a) (x – b)

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##### Question 76:

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##### Question 77:

Find the derivative of :

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##### Question 78:

Find the derivative of :

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##### Question 79:

Find the derivative of :

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##### Question 80:

Find the derivative of :

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##### Question 81:

Find the derivative of :

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##### Question 82:

Find the derivative of :

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##### Question 83:

Find the derivative of cos x from first principle.

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##### Question 84:

Find the derivatives of the following functions :

sin x cos x

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##### Question 85:

Find the derivatives of the following functions :

sec x

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##### Question 86:

Find the derivatives of the following functions :

5 sec x + 4 cos x

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##### Question 87:

Find the derivatives of the following functions :

cosec x

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##### Question 88:

Find the derivatives of the following functions :

3 cot x + 5 cosec x

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##### Question 89:

Find the derivatives of the following functions :

5 sinx – 6 cos x + 7

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##### Question 90:

Find the derivatives of the following functions :

2 tan x – 7 sec x