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Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce PDF Download

 limit of Trigonometric Functions

(a) Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce = 1 (approach from left side)

(b) Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce = 1 (approach from right side)

(c)Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce = 1

(d) Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce = 1

[Where x is measured in radians]

Ex.17 Find Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol. 

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Ex.18 Evaluate : Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 Sol.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Ex.19 Solve Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol. 

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Note : Limit Using Expansion of Functions

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Ex.20 Find Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Ex.21 Find Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol.

This is of the form 0/0 if we put x = 1. Therefore we put x = 1 + h and expand.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Ex.22 Evaluate Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Ex.23 Let f(x) be a function such that Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce Find the values of a and b such that Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

R.H.S. is finite then L.H.S. is also finite, then 1 + a –b = 0  and Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

 

Ex.24 If the Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce exists and has the value equal to l, then find the value of Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Sol.

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce Use binomial expansion to get the following relations :

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

The document Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce is a part of the Commerce Course Mathematics (Maths) Class 11.
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FAQs on Limits of Trigonometric Functions - Mathematics (Maths) Class 11 - Commerce

1. What are the limits of sin(x) and cos(x) as x approaches infinity?
Ans. The limits of sin(x) and cos(x) as x approaches infinity do not exist. Both functions oscillate between -1 and 1 infinitely, without converging to a specific value.
2. Can the limit of tan(x) as x approaches infinity be determined?
Ans. No, the limit of tan(x) as x approaches infinity does not exist. The tangent function becomes unbounded and oscillates between negative and positive infinity as x approaches infinity.
3. What is the limit of sin(x)/x as x approaches 0?
Ans. The limit of sin(x)/x as x approaches 0 is 1. This result is known as the Squeeze Theorem or the Fundamental Theorem of Calculus.
4. Are there any limits for the cotangent function?
Ans. Yes, the limit of cot(x) as x approaches 0 is infinity, and the limit of cot(x) as x approaches infinity is 0. These limits can be derived using the reciprocal properties of the cotangent function.
5. What is the limit of sec(x) as x approaches pi/2?
Ans. The limit of sec(x) as x approaches pi/2 does not exist. The secant function becomes unbounded as x approaches pi/2, oscillating between negative and positive infinity.
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