Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ 1cos x x = lim x0 sin x x 1cos x lim x0 = x sin x lim x0 x = 0 1cos x sin x lim 0and lim 1 1 x0 x x0 x = 0 Question 22: tan 2x lim x 2 x 2 Solution 22: tan 2x lim x 2 x 2 0 At x = , the value of the given function takes the form 2 0 Now, put x y So that x , y 0 2 2 tan2 y tan2x 2 lim lim x y0 y 2 x 2 tan 2y = lim y 0 y tan2y = lim tan 2y tan2y y0 y sin2y = lim y0 y cos2 y = sin2y 2 y lim y0 2 y cos2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ sin2y 2 = lim lim 2y0 2y y0 cos2 y 2 sin x = 1 lim 1 cos0 x0 x 2 = 1 1 y02y 0 = 2 Question 23: Find lim f(x) and x 0 Solution 23: The given function is 2x3, x0 f(x) = 3x1, x0 lim f(x), where f(x) = x 1 x lim f x lim 2 3 2 0 3 3 x0 x0 x lim f x lim3 1 3 0 1 3 x0 x0 lim f x lim f x lim f x 3 x0 x0 x0 x lim f x lim3 1 3 1 1 6 x1 x1 lim f x lim f x lim f x 6 x1 x1 x1 2x3, x0 3x1, x0 Question 24: Find lim f x , when f(x) = x 1 Solution 24: The given function is f(x) = 2 x x 2 x x 1, 1 1, 1 2 2 x x1 x1 2 x x 2 x x lim f x lim 1 1 1 1 1 0 1, 1 1, 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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