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
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