Careers360 Logo
Engineering and Architecture
Search Colleges, Exams, Schools & more
100 Marks in JEE Main 2025: Check Your Expected Percentile
  1. Home
  2. JEE Main
  3. Study Material
  4. Limits of the form (1 power infinity) - Practice Questions & MCQ

Limits of the form (1 power infinity) - Practice Questions & MCQ

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

Quick Facts

  • Limits of the form (1 power infinity) is considered one the most difficult concept.

  • 206 Questions around this concept.

Solve by difficulty

QuestionEASY

\lim_{x\rightarrow \infty }\left ( \frac{x^{2}+5x+3}{x^{2}+x+3} \right )^{\frac{1}{x}}

View Solution

If \lim_{x\rightarrow \infty }\left ( 1+\frac{a}{x}+\frac{b}{x^{2}} \right )^{2x}= e^{2}, then the values of a and b are

View Solution

Let p= \lim_{x\rightarrow 0+}\left ( 1+\tan ^{2} \sqrt{x}\right )^{\frac{1}{2x}}then  log p
is equal to :

View Solution

limx→0(1+x)1/x−exequals

View Solution

Concepts Covered - 1

Limits of the form (1 power infinity)

Limits of the form 1∞ (1 power infinity)

To find the limit of the form 1∞, we will use the following results
If limx→af(x)=limx→ag(x)=0
Then,

limx→a[1+f(x)]1g(x)=elimx→af(x)g(x)
Or
When, limx→af(x)=1 and limx→ag(x)=∞
Then,

limx→a[f(x)]g(x)=limx→a[1+(f(x)−1)]g(x)=elimx→a(f(x)−1)g(x)

Proof: 

Let L=limx→a[1+f(x)]1g(x)
Taking logs of both sides

log⁡(L)=log⁡(limx→a[1+f(x)]1g(x))log⁡(L)=limx→a1g(x)log⁡(1+f(x))log⁡(L)=limx→a1g(x)(log⁡(1+f(x))f(x))⋅f(x)
As f(x) is tending to 0 , so

log⁡(L)=limx→af(x)g(x)L=elimx→af(x)g(x)2

Some particular cases  

(a) limx→0(1+x)1x=e
(b) limx→∞(1+1x)x=e
(c) limx→0(1+cx)1x=ec
(d) limx→∞(1+cx)x=ec

Study it with Videos

Limits of the form (1 power infinity)

Study other Related Concepts

Limits of the form (1 power infinity) Current Topic

Limit
Left-Hand Limits and Right-Hand Limits
Algebra of Limits
Limit of Indeterminate Form and Algebraic limit
Limit of Algebraic function
Limit Using Expansion
Sandwich Theorem
Limits of Trigonometric Functions
Exponential and Logarithmic Limits
Limits of the form (1 power infinity)

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

Books

Reference Books

Limits of the form (1 power infinity)

Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus

Page No. : 2.26

Line : 32

Clear your Basics with NCERT

E-books & Sample Papers

Get Answer to all your questions

JEE Main Articles

JEE Main Score Card 2025 Session 2: Download Link, Steps to Check
Apr 15, 2025
JMI Jamia Millia Islamia JEE Main Cutoff
Apr 15, 2025
JEE Main Result 2025 Session 2 - Date (By April 17), Direct Link, BE, BTech Scorecard at jeemain.nta.nic.in
Apr 15, 2025
JEE Main Rank vs College 2025: Admission Chances in Top Engineering Colleges
Apr 15, 2025
JEE Main April Result 2025 - Link, Download Rank Card at jeemain.nta.ac.in
Apr 15, 2025
JEE Mains Marks Calculator 2025 - Estimate Your Score and Percentile
Apr 14, 2025
What is Percentile in JEE: Understanding Calculation, Rank & Importance
Apr 14, 2025
85 Percentile in JEE Mains 2025: How Many Marks, Subject Wise Percentile
Apr 14, 2025

B.Tech/B.Arch Admissions OPEN

Amity University Noida B.Tech Admissions 2025
Apply

Among Top 30 National Universities for Engineering (NIRF 2024) | 30+ Specializations | AI Powered Learning & State-of-the-Art Facilities

UPES B.Tech Admissions 2025
Apply

Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements | Last Date to Apply: 28th April

Symbiosis-SITEEE-2025
Apply

Gateway for admissions to Engineering courses @ Symbiosis | NAAC A++ Grade | Among top 31 in India (NIRF 2024)

Chandigarh University Admissions 2025
Apply

Ranked #1 Among all Private Indian Universities in QS Asia Rankings 2025 | Scholarships worth 210 CR

Lovely Professional University B.Tech Admissions 2025
Apply

India's Largest University | NAAC A++ Accredited | 100% Placement Record | Highest Package Offered : 2.5 Cr PA | Application End Date: 15th Apr'25

BML Munjal University | B.Tech Admissions 2025
Apply

A Hero Group Initiative | Up to 100% Scholarships | Highest CTC 32.99 LPA | Average CTC 8.45 LPA | Accepts JEE Score | Last Date: 19th Apr'25

View All Application Forms
News and Notifications
3 days ago :
April 03, 2025 - 12:52 PM IST :
March 28, 2025 - 10:35 PM IST :
JEE Main Result 2025 Live: NTA April attempt results, final answer key at jeemain.nta.nic.in soon; cut-off
April 15, 2025 - 03:45 PM IST
JEE Main response sheet 2025 'blank', answers marked shown differently
April 15, 2025 - 01:14 PM IST
JEE Main Result 2025: BTech CSE cut-offs go up for OBC candidates at top NITs
April 15, 2025 - 11:07 AM IST
JEE Main 2025 session 2 answer key challenge facility ends today; how to raise objections
April 13, 2025 - 07:15 AM IST
JEE Main Answer Key 2025 (Out) Live: NTA JEE Mains session 2 response sheet out; answer key updates, cut-offs
April 12, 2025 - 10:28 PM IST
JEE Main Eligibility: Marks in 12th subjects for 2025 admissions to NITs, IIITs, CFTIs
April 12, 2025 - 01:04 PM IST
NTA issues JEE Main 2025 session 2 provisional answer key, response sheet on jeemain.nta.nic.in
April 12, 2025 - 06:32 AM IST
Ask
Question
Ask

Student Community: Where Questions Find Answers

Ask and get expert answers on exams, counselling, admissions, careers, and study options.
Download Careers360 App
All this at the convenience of your phone

  • Regular Exam Updates

  • Best College Recommendations

  • College & Rank predictors

  • Detailed Books and Sample Papers

  • Question and Answers

Scan and download the app

OR

Joint Entrance Examination (Main)      
JEE Main 2025 Rank Predictor
Back to top