Careers360 Logo
How should preparation strategies differ for JEE Main and JEE Advanced 2025

Limits of Trigonometric Functions - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Trigonometric Limits is considered one the most difficult concept.

  • 641 Questions around this concept.

Solve by difficulty

\lim_{x\rightarrow \frac{\pi }{2}}\: \: \frac{\cot x-\cos x}{\left ( \pi -2x \right )^{3}}equals:

\lim_{x\rightarrow 0}\frac{\sin \left ( \pi \cos ^{2}x \right )}{x^{2}}   is equal to :

if f(x) is continuous and f(\frac{9}{2})=\frac{2}{9}, then \lim_{x\rightarrow 0}f\left ( \frac{1-\cos 3x}{x^{2}} \right )  is equal to :

\lim_{x\rightarrow 2}\left ( \frac{\sqrt{1-\cos \left \{ 2(x-2) \right \}}}{x-2} \right )

If a=limx01+1+x42x4 and b=limx0sin2x21+cosx, then the value of ab3 is :

limx0cos2xcos4xx2 equals

limx0sin8xtan3x equals

UPES B.Tech Admissions 2025

Ranked #42 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements | Last Date to Apply: 15th May

ICFAI University Hyderabad B.Tech Admissions 2025

Merit Scholarships | NAAC A+ Accredited | Top Recruiters : E&Y, CYENT, Nvidia, CISCO, Genpact, Amazon & many more

limx0sin3x+sinxx=

limθπ2(secθtanθ)

JEE Main 2025 College Predictor
Know your college admission chances in NITs, IIITs and CFTIs, many States/ Institutes based on your JEE Main rank by using JEE Main 2025 College Predictor.
Use Now

limx1(1+cosπx)cot2πx

Concepts Covered - 1

Trigonometric Limits

Trigonometric Limits

In the trigonometric limit, apart from using the method of direct substitution, factorization and rationalization (same as given in algebraic limits), we can use the following formulae.

(i) limx0sinxx=1
(ii) limx0tanxx=1

As limx0tanxx=limx0sinxx×1cosx

=limx0sinxx×limx01cosx=1×1

(iii) limxasin(xa)xa=1

As limxasin(xa)xa=limh0sin((a+h)a)(a+h)a

=limh0sinhh=1

(iv) limxatan(xa)xa=1
(v) limxasin(f(x))f(x)=1, if limxaf(x)=0

Similarly, limxatan(f(x))f(x)=1, if limxaf(x)=0
(vi) limx0cosx=1

(vii) limx0sin1xx=1

As limx0sin1xx=limy0ysiny[sin1x=y]
=1
(viii) limx0tan1xx=1

Study it with Videos

Trigonometric Limits

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Trigonometric Limits

Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus

Page No. : 2.17

Line : 13

E-books & Sample Papers

Get Answer to all your questions

Back to top