English
Hindi

Question

Download Solution PDF

Function f(x) = (x + 1)cotx will be continuous at x = 0 if the value of f(0) is

This question was previously asked in
UP TGT Mathematics 2021 Official Paper
Download PDF Attempt in App
View all UP TGT Papers >
  2. 0
  3. e
  4. 1

Answer (Detailed Solution Below)

Option 3 : e
Free Tests
View all Free tests >
Free
UP TGT Hindi FT 1
125 Qs. 500 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

A function is said to be continuous if 

Calculation:

Given:

f(x) = (x + 1)cotx 

Taking log on both sides

log (f(x)) = cot x log (x + 1)

For checking continuity at x = 0

 = 0/0 form

Using L-Hospital rule

⇒ log (f(0)) = 1

⇒ f(0) = e1 = e

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 Continuity Questions

Q1.The function f, given by \(f(x)={\left\{ \begin{array}{rcl} {sin\ x^2\over x}, & \mbox{x ≠ 0} \\ 0, & x=0 \\ \end{array}\right.}\) is
Q2.If f ∈ R [a, b], consider the following statements : (a) 'f' is continuous on [a, b]  (b) 'f' is monotonic on [a, b] Which of the following is correct?
Q3.Function f(x) = (x + 1)cotx will be continuous at x = 0 if the value of f(0) is
Q4.If 0 < x < 1, which of the following terms increases as x increases? (i) 1 – x3 (ii) x – 1 (iii) 1/x2
Q5.The function \(f(x)=\frac{4-x^2}{4x-x^3}\) is
Q6.The function \(f(x) = \frac{{In~x ~+~ {{\tan }^{ - 1}}x}}{{{x^2} - 1}}\) is:
Q7.A function f(x) is continuous in the interval [0, 2]. It is known that f(0) = f(2) =-1 and f(1) = 1. Which one of the following statements must be true?
Q8.The values of x for which the function \(f\left( x \right) = \frac{{{x^2} - 3x - 4}}{{{x^2} + 3x - 4}}\) is NOT continuous are
Q9.Let \(g\left( x \right) = \left\{ {\begin{array}{*{20}{c}} { - x,}&{x \le 1}\\ {x + 1,}&{x \ge 1} \end{array}} \right.\) and \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 - x,}&{x \le 0}\\ {{x^2},}&{x > 0} \end{array}} \right.\). Consider the composition of f and g, i.e. (fog)(x) = f(g(x)). The number of discontinuities in (fog)(x) present in the interval (-∞, 0) is:

More Calculus Questions

Q1.Consider a cube having the dimension x, y, z ∈ [1, 3]. If a B̅ = \(2 x^{2} y \hat{a}_{x}+3 x^{2} y^{2} \hat{a}_{y}\). Divergence of B̅ at the centre of cube is :
Q2.Three vectors \(\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}\) and \(\overrightarrow{\mathrm{r}}\) are given as \(\overrightarrow{\mathrm{p}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}} \) \(\overrightarrow{\mathrm{q}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \) \(\overrightarrow{\mathrm{r}}=2 \hat{i}+3 \hat{j}+4 \hat{k}\) Which of the following is/are CORRECT?
Q3.Let 𝑓, 𝑔 ∶ ℝ2 → ℝ be defined by 𝑓(𝑥, 𝑦) = \(\rm x^2-\frac{3}{2}xy\) and 𝑔(𝑥, 𝑦) = 4𝑥4 − 5𝑥2𝑦 + 𝑦2  for all (𝑥, 𝑦) ∈ ℝ2 . Consider the following statements: 𝑃: 𝑓 has a saddle point at (0,0). 𝑄: 𝑔 has a saddle point at (0,0). Then
Q4.A vector \(\vec{P}\) is given by \(\vec{P}\) = \(x^3 \vec{a_x}-x^2 y^2 \vec{a_y}-x^2 y z \vec{a_z}\). Which one of the following statements is correct?
Q5.The work done by two forces \(\vec{P}=3 \hat{i}-2 \hat{j}+\hat{k}\) and \(\vec{Q}=\hat{i}+3 \hat{j}-5 \hat{k}\), in displacing a particle from point A, whose position vector is \(-2 \hat{i}+5 \hat{k}\), to point B, whose position vector is \(3 \hat{i}-7 \hat{j}+2 \hat{k}\), is
Q6.\(\int x^{n} d x=\frac{x^{n+1}}{n+1}+c\) is not true, if n is equal to
Q7.The gradient of the normal to the curve y = 2x2 + 3sin x at x = 0 is
Q8.Writing Lagrange’s mean value theorem as f(b) - f(a) = (b - a)f'(c), a < c < b the value of c, if f(x) = x(x - 1), a = 0, \(b = \frac{1}{2}\), is
Q9.Evaluate the definite integration \(\int_1^2\) x . dx and choose the right answer:
Q10.Evaluate the definite integration \(\int_a^b\) ex ⋅ dx:
Suggested Test Series
View All >
UP TGT Mock Test Series 2025
444 Total Tests with 6 Free Tests
Start Free Test
Social Science (SST) Content for All Teaching Exams - Let's Crack TET!
191 Total Tests with   1 Free Tests
Start Free Test

UP TGT Important Links

Syllabus and Exam PatternEligibility CriteriaAdmit CardAnswer KeyAnswer KeyCut Off

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
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 go teen patti list teen patti neta teen patti master golden india