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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 :
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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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