English
Hindi

Question

Download Solution PDF

Examine the continuity of a function f(x) = (x - 2) (x - 3)

  1. Discontinuous at x = 2
  2. Discontinuous at x = 2, 3
  3. Continuous everywhere
  4. Discontinuous at x = 3

Answer (Detailed Solution Below)

Option 3 : Continuous everywhere
Free Tests
View all Free tests >
Free
UP TGT Arts Full Test 1
125 Qs. 500 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

  • We say f(x) is continuous at x = c if

LHL = RHL = value of f(c)

i.e., 

Calculation:

            (a ϵ Real numbers)

∴ f(x) = f(a), So continuous at everywhere

Important tip:

Quadratic and polynomial functions are continuous at each point in their domain

Download Solution PDF
Latest UP TGT Updates

Last updated on May 6, 2025

-> The UP TGT Exam for Advt. No. 01/2022 will be held on 21st & 22nd July 2025.

-> The UP TGT Notification (2022) was released for 3539 vacancies.

-> The UP TGT 2025 Notification is expected to be released soon. Over 38000 vacancies are expected to be announced for the recruitment of Teachers in Uttar Pradesh. 

-> Prepare for the exam using UP TGT Previous Year Papers.

Exams Tests Super Practice

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 >
UP TGT Mock Test Series 2025
444 Total Tests with 3 Free Tests
Start Free Test
Pedagogy for All Teaching Exams (Paper 1 & 2) - Let's Crack TET!
345 Total Tests with   3 Free Tests
Start Free Test

UP TGT Important Links

Syllabus and Exam PatternEligibility CriteriaAdmit CardAnswer KeyAnswer KeyCut Off

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 bindaas teen patti real money app teen patti real master teen patti