Limits of Trigonometric Functions

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

limit of Trigonometric Functions

(a)  = 1 (approach from left side)

(b)  = 1 (approach from right side)

(c) = 1

(d)  = 1

[Where x is measured in radians]

Ex.17 Find

Sol.

Ex.18 Evaluate :

Sol.

Ex.19 Solve

Sol.

Note : Limit Using Expansion of Functions

Ex.20 Find

Sol.

Ex.21 Find

Sol.

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

Ex.22 Evaluate

Sol.

Ex.23 Let f(x) be a function such that  Find the values of a and b such that

Sol.

R.H.S. is finite then L.H.S. is also finite, then 1 + a –b = 0  and

Ex.24 If the  exists and has the value equal to l, then find the value of

Sol.

Use binomial expansion to get the following relations :

The document Limits of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce is a part of the Commerce Course Mathematics (Maths) Class 11.
All you need of Commerce at this link: Commerce

## Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

## 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.

## Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

### Up next

 Explore Courses for Commerce exam

### Top Courses for Commerce

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;