Ex 5.1, 25 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 5.1, 25 Examine the continuity of f, where f is defined by = sin , 0 & 1, =0 = sin , 0 & 1, =0 Case 1: At x = 0 f (x) is continuous at x = 0 if LHL = RHL = f(0) l x 0 = l x 0 = 0 And f(x) = sin x cos x f(0) = sin 0 cos 0 = 1 Hence, L H L = R H L = f(0) f (x) is continuous at x = 0 Case 2: For x 0 f(x) = sin x cos x Let p (x) = sinx & q (x) = cos x We know that, sin x & cos x are both continuous functions So, p(x) & q (x) is continuous at all real numbers By Algebra of continuous functions, If & both continuous for all real number , then f(x) = p(x) q(x) is continuous at all real numbers f(x) = sin x cos x is continuous for all real numbers. Hence, f(x) is continuous at all points
Ex 5.1
Ex 5.1 ,1
Ex 5.1 ,2
Ex 5.1 ,3
Ex 5.1 ,4
Ex 5.1 ,5
Ex 5.1 ,6
Ex 5.1 ,7
Ex 5.1 ,8
Ex 5.1, 9 Important
Ex 5.1, 10
Ex 5.1, 11
Ex 5.1, 12
Ex 5.1, 13 Important
Ex 5.1, 14
Ex 5.1, 15
Ex 5.1, 16 Important
Ex 5.1, 17
Ex 5.1, 18 Important
Ex 5.1, 19
Ex 5.1, 20
Ex 5.1, 21
Ex 5.1, 22
Ex 5.1, 23
Ex 5.1, 24
Ex 5.1, 25 You are here
Ex 5.1, 26
Ex 5.1, 27
Ex 5.1, 28 Important
Ex 5.1, 29
Ex 5.1, 30 Important
Ex 5.1, 31
Ex 5.1, 32
Ex 5.1, 33
Ex 5.1, 34 Important
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.