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

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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

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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