Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More

Question

Download Solution PDF

If \(f(x)=\frac{x+|x|}{x}\), then the value of \(\displaystyle\lim _{x \rightarrow 0} f(\mathbf{x})\) is

This question was previously asked in
VITEEE PYP_125Qs150Min125Marks
Attempt Online
View all VITEEE Papers >
  1. 0
  2. 2
  3. does not exist
  4. None of these

Answer (Detailed Solution Below)

Option 3 : does not exist
Free Tests
View all Free tests >
Free
JEE Main 2025 (Session II) All India Live Test
4 K Users
75 Questions 300 Marks 180 Mins
Start Now

Detailed Solution

Download Solution PDF

Calculation

LHL = \(\displaystyle\lim _{h \rightarrow 0} \frac{-h+|h|}{-h}\) =  0

RHL =\(\displaystyle\lim _{h \rightarrow 0} \frac{h+|h|}{h}\) = 2

LHL ≠ RHL ⇒ limit does not exist

Hence option 3 is correct

Download Solution PDF
Latest VITEEE Updates

Last updated on Jul 3, 2025

->Vellore Institute of Technology will open its application form for 2026 on November 4, 2025.

->The VITEEE 2026 exam is scheduled to be held from April 20, 2026 to April 27, 2026.

->VITEEE exams are conduted for admission to undergraduate engineering programs at the Vellore Institute of Technology (VIT) and its affiliated campus.

->12th pass candidates can apply for the VITEEE exam.

‹‹ Previous Ques
Next Ques ››

More Evaluation of Limits Questions

Q1.What is \(\rm \lim_{x\rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)\) equal to? 
Q2.Which one of the following is correct regarding \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)?
Q3.The number of distinct integer values of n satisfying: \(\rm \frac{4-\log_2n}{3-\log_4n}<0\) is
Q4.\(\rm \displaystyle \lim_{\theta\rightarrow 0}\frac{1-\cos m \theta}{1-\cos n\theta}=?\)
Q5.\(\rm \displaystyle\lim_ {x\rightarrow 0}\left({\frac{\sqrt{1-cosx^2}}{(1-cosx)}}\right)\)
Q6. \(\rm \displaystyle\lim_ {x\rightarrow 1}\left({\frac{\sqrt{1-cos2(x-1)}}{(x-1)}}\right)\)
Q7.Sum of the series from n = 1 to ∞, whose nth term is \(\rm\frac{1}{(n+1)!}\) is
Q8.\(\rm\displaystyle\lim _{x \rightarrow 0}\frac{e^x−1−x−x^2}{x^2}\) =
Q9.Sum of the series \(1+\frac{2^2}{1 !}+\frac{3^2}{2 !}+\frac{4^2}{3 !}+\ldots \ldots.\) is
Q10.Which of the following has the highest value?

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 : 

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?
Exams
Board Exams
Syllabus
Test Series
Previous Year Papers
Cut Off
Eligibility
Important Exams
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
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
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti star teen patti fun teen patti master downloadable content teen patti live