English
Hindi

Question

Download Solution PDF

The value of  is

  1. 1
  2. -1
  3. 0
  4. Does not exist

Answer (Detailed Solution Below)

Option 4 : Does not exist
Free Tests
View all Free tests >
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

For a limit to exist, Left-hand limit and right-hand limit must be equal.

Calculations:

For a limit to exist Left-hand limit and right-hand limit must be equal.

|x| can have two values 

|x | = - x when x is negative 

|x| = x when x is positive.

 = 

​​ = 

Here, 

Hence, does not exist. 

Download Solution PDF
Latest NDA Updates

Last updated on Jun 18, 2025

->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Exams Tests Super Practice

More Existence of a Limit Questions

Q1.Let \(\rm f(x) = \left\{\begin{matrix} 1+\frac{x}{2k}, & 0 < x < 2\\\ kx, & 2 \le x < 4 \end {matrix}\right.\) If \(\displaystyle\lim_{x\rightarrow 2}\) f(x) exists, then what is the value of k?
Q2.Consider the following: 1. \(\rm \underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}\) exists. 2. \(\rm \underset{x\to 0}{\mathop{\lim }}\, e^{\frac 1 x}\) does not exist. Which of the above is / are correct?
Q3.Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If \(\lim_{x \rightarrow 0} \left[1 + \frac {f(x)} {x^2} \right] = 3\) then f(2) is?
Q4.If f(x) is continuous at x = a then  \(\rm \displaystyle\underset{x\to a}{\mathop{\lim }}\rm\,f\left( x \right)\) 
Q5.The value of \(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{|x|}{x}\) is
Q6.Evaluate: \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{{x^3} \cdot \cot x}}{{1 - \cos x}}} \right)\)
Q7.Consider the following statements: 1. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) both exist, then \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists. 2. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists, then both \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) must exist. Which of the above statements is/are correct?

More Limit and Continuity Questions

Q1.Consider the following statements :  I. f(x) is continuous at x = 0.  Il. f(x) is continuous at x = 1  Which of the statements given above is/are correct? 
Q2.What is f(0.999) + f(1.001) equal to
Q3.What is \(\rm \lim_{x\rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)\) equal to? 
Q4.Which one of the following is correct regarding \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)?
Q5.\(\lim _{x \rightarrow 0} \frac{\int_0^{x^2}(\sin \sqrt{t}) d t}{x^3}\) is equal to : 
Q6.If f : R → R is a function defined by f(x) = [x – 1] cos ((2x – 1)/2)π, where [.] denotes the greatest integer function, then f is:
Q7.\(\lim _{n \rightarrow \infty}\left(\left(\frac{n}{n+1}\right)^α+\sin \frac{1}{n}\right)^n\) where α ∈ Q is equal to  
Q8.If \(\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0\) then 8(α + β) is equal to
Q9.Let f : R → be a function given by \(f(x) = \left\lbrace \begin{matrix} \frac{1-\cos 2x}{x^2} & , & x < 0 \\\ α & , & x = 0 \\\ \frac{β \sqrt{1-\cos x}}{x} & , & x>0 \end{matrix} \right.\), where α, β ∈ R. If f is continuous at x = 0, then α2 + β2 is equal to: 
Q10.If the function \(\rm f(x)=\frac{\sin 3x+\alpha \sin x-\beta \cos 3x}{x^3}\) x ∈ R is continuous at x = 0, then f(0) is equal to : 
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 4 Free Tests
Start Free Test
Current Affairs (CA) 2024 Mega Pack for SSC/Railways/State Exam Mock Test
427 Total Tests with   5 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master gold apk teen patti live mpl teen patti teen patti game - 3patti poker