Ex 12.1, 28 - Chapter 13 Class 11 Limits and Derivatives (Important Question)

Last updated at Dec. 16, 2024 by

Slide59.JPG

Slide60.JPG

Go Ad-free

Transcript

Ex 12.1, 28 Suppose f(x) = {█(a+bx, x<1@4, x=1@b−ax, x>1)┤ and if lim┬(x→1) f(x) = f(1) what are possible values of a and b? Here, limit exist at x → 1 i.e., LHL = RHL = f(1) = 4 LHL at x → 1 lim┬(x→1^− ) f(x) = lim┬(h→0) f(1 − h) = lim┬(h→0) a + b (1 − h) = a + b (1 − 0) = a + b RHL at x → 1 lim┬(x→1^+ ) f(x) = lim┬(h→0) f(1 + h) = lim┬(h→0) b − a (1 + h) = b − a (1 + 0) = b − a From (1) and (2) a + b = 4 From (1) and (3) b − a = 4 Adding both a + b + b − a = 4 + 4 2b = 8 b = 4 Also, a + b = 4 a + 4 = 4 a = 0

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo