Exercise 5.1 class 12

Transcript Ex 5.1, 3 Examine the following functions for continuity. (c) f (x) = (𝑥^(2 )− 25 )/(𝑥 + 5), x ≠ –5 f (x) = (𝑥^(2 )− 25 )/(𝑥 + 5) Putting x = –5 f (−5) = (〖(−5)〗^(2 )− 25 )/(−5 + 5) = (25− 25 )/(−5 + 5) = 0/0 = Undefined Hence, f(x) is not defined at x = −5 So, we check for continuity at all points except −5 Let c be any real number except −5. f is continuous at 𝑥 = 𝑐 if (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) LHS (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) (𝑥^2− 25)/(𝑥 + 5) = lim┬(x→𝑐) ((𝑥 − 5) (𝑥 + 5))/(𝑥 + 5) = lim┬(x→𝑐) 𝑥−5 Putting x = c = c − 5 RHS f (c) = (𝑐^(2 )− 25 )/(𝑐 + 5) = ((𝑐 − 5)(𝑐 + 5))/((𝑐 + 5)) = c − 5 Let c be any real number except −5. f is continuous at 𝑥 = 𝑐 if (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (except −5) Thus, we can write that f is continuous for all real numbers except −5 ∴ f is continuous at each 𝐱 ∈ R − Show More

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.1 are part of • • • • • • • Board CBSE Textbook NCERT Class Class 12 Subject Maths Chapter Chapter 5 Chapter Name Continuity and Differentiability Exercise Ex 5.1 Number of Questions Solved 34 Category NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exc 5.1 Ex 5.1 Class 12 Maths Question 1. Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5. Solution: (i) At x = 0. lim x–>0 f (x) = lim x–>0 (5x – 3) = – 3 and f(0) = – 3 ∴f is continuous at x = 0 (ii) At x = – 3, lim x–>3 f(x)= lim x–>-3 (5x – 3) = – 18 and f( – 3) = – 18 ∴ f is continuous at x = – 3 (iii) At x = 5, lim x–>5 f(x) = lim x–>5 (5x – 3) = 22 and f(5) = 22 ∴ f is continuous at x = 5 Ex 5.1 Class 12 Maths Question 2. Examine the continuity of the function f(x) = 2x² – 1 at x = 3. Solution: lim x–>3 f(x) = lim x–>3 (2x² – 1) = 17 and f(3)= 17 ∴ f is continuous at x = 3 Ex 5.1 Class 12 Maths Question 3. Examine the following functions for continuity. (a) f(x) = x – 5 (b) f(x) = \(\\ \frac \) to is a continuous function. Solution: Ex 5.1 Class 12 Maths Question 31. Show that the function defined by f(x)=cos (x²) is a continuous function. Solution: Now, f (x) = cosx², let g (x)=cosx and h (x) x² ∴ goh(x) = g (h (x)) = cos x² Now g and h both are continuous ∀ x ∈ R. f (x) = goh (x) = cos x² is also continuous at all x ∈ R. Ex 5.1 Class 12 Maths Question 32. Show that the...

NCERT Solutions Class 12 Maths Chapter 5 Exercise 5.1 Continuity and Differentiability The problems provided in NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1 Continuity and Differentiability focus on continuous functions and their algebra. A real-valued function is continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function is continuous if it is continuous on the whole of its domain. The Learning the fundamentals of Continuity of functions and their arithmetic operations is important for every student. It is a basic building block required for learning the vast topic of calculus. Class 12 Maths NCERT Solutions Chapter 5 has 34 sums related to examining and determining the continuity of various functions. Students can easily learn and practice with the NCERT Solutions Class 12 Chapter 5 Exercise 5.1 as given below. ☛ Download NCERT Solutions Class 12 Maths Chapter 5 Exercise 5.1 Exercise 5.1 Class 12 Chapter 5 Download PDF More Exercises in Class 12 Maths Chapter 5 • • • • • • • • NCERT Solutions Class 12 Maths Chapter 5 Exercise 5.1 Tips Learning about the continuity of functions and their operations is essential to build several advanced concepts in calculus. Exercise 5.1 of Chapter 5 Continuity and Differentiability consists of many examples and sums devised to engraft the basic knowledge of continuity. With the detailed practice of all the questions present in the Analyzing the no...

NCERT Solutions for Class 12 Maths Exercise 5.1 Continuity and Differentiability: Continuity and Differentiability is the fifth chapter in CBSE Class 12 Maths. It is one of the most important chapters in CBSE Class 12 Maths and requires plenty of practice for students to ace the Board exams. The NCERT Solutions for Continuity and Differentiability Class 12 Exercise 5.1 Maths will help students get the best solutions for the first exercise of Chapter 5 in the NCERT textbook. CBSE Class 12 Maths Exercise 5.1 talks about the Introduction, Continuity and Algebra of Continuous Functions. Embibe provides more than 400 practice questions for all the sub-topics involved in chapter 5 of Class 12 Maths. To score the best marks in Maths, students must practice all the questions without fail. Keep reading to find out NCERT solutions for Class 12 Chapter 5.1 Continuity and Differentiability. NCERT Solutions for Class 12 Maths Chapter 5: Important Topics Continuity and Differentiability is one of the important topics of Class 12 Maths. Practicing the problems of Chapter 5 not only helps students to score good marks in the final exams. It also helps them to ace the entrance exams. Once the students start solving problems related to chapter 5, they can easily score good marks in the exams. Students must practice as many questions as possible so that they can analyse the nature of the questions asked in the exam. Embibe delivers the solutions to all the questions of Class 12 Maths Chapter ...

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1 NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1 – Free PDF Download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability, contains solutions for all Exercise 5.1 questions. These NCERT Solutions are prepared with the help of subject experts based on the latest CBSE syllabus. Students can download the Access Answers of Maths NCERT Class 12 Chapter 5 Continuity and Differentiability Exercise 5.1 Page number 159

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions for Class 12 Maths Chapter 5 – Free PDF Download The NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability provide solutions to all the questions under the chapter (All Exercises and Miscellaneous Exercise solutions). These Subject experts at BYJU’S have created the NCERT Solutions for Class 12 Maths to help students while solving or practising problems. Further, all the solutions are in accordance with the latest CBSE Syllabus. Students can download the PDF of the Access answers of NCERT Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability offer all Exercises and Miscellaneous Exercise solved questions listed under the chapter in a systematic manner. These NCERT Solutions are solved by subject experts & prepared according to the prescribed CBSE curriculum’s latest syllabus. So, Students can rely on these NCERT Solutions of Class 12 maths chapter 5 and brush up their basics knowledge. From this page, you can download Class 12 Maths Chapter 5 NCERT Solutions PDF with ease. Preparing from the Class 12 Maths Ch 5 Continuity and Differentiability NCERT Solutions assists students to solve problems within exam duration. Besides, you will also know how to solve various questions which is an extra addon while your preparation. Students can score high in the exams with the NCERT Solutions for Class 12 Maths Ch 5 as it covers all concepts for your thorough preparation. Class 12 Maths NCERT Solutions Chapter 5 Continuity and Differentiability In chapter 5, Students will learn the concept called continuity and differentiability. In Continuity and Differentiability, you have to deal with the questions based on determining an equation is continuous if furnished with different values of ‘x’. Also, you will explore some functions of continuity and generate conclusions. Moreover, you can come across with explanations for different types of questions from the main topics covered in NCERT Solutions for Class 12, Chapter 5- Continuity and Differentia...

Previous Next  Access Answers to NCERT Solutions Class 7 Maths Chapter 5 – Lines and Angles Exercise 5.1 1. Find the complement of each of the following angles: (i) Solution:- Two angles are said to be complementary if the sum of their measures is 90 o. The given angle is 20 o Let the measure of its complement be x o. Then, = x + 20 o = 90 o = x = 90 o – 20 o = x = 70 o Hence, the complement of the given angle measures 70 o. (ii) Solution:- Two angles are said to be complementary if the sum of their measures is 90 o. The given angle is 63 o Let the measure of its complement be x o. Then, = x + 63 o = 90 o = x = 90 o – 63 o = x = 27 o Hence, the complement of the given angle measures 27 o. (iii) Solution:- Two angles are said to be complementary if the sum of their measures is 90 o. The given angle is 57 o Let the measure of its complement be x o. Then, = x + 57 o = 90 o = x = 90 o – 57 o = x = 33 o Hence, the complement of the given angle measures 33 o. 2. Find the supplement of each of the following angles: (i) Solution:- Two angles are said to be supplementary if the sum of their measures is 180 o. The given angle is 105 o Let the measure of its supplement be x o. Then, = x + 105 o = 180 o = x = 180 o – 105 o = x = 75 o Hence, the supplement of the given angle measures 75 o. (ii) Solution:- Two angles are said to be supplementary if the sum of their measures is 180 o. The given angle is 87 o Let the measure of its supplement be x o. Then, = x + 87 o = 180 o = ...