CLASS_11_MATHS_SOLUTIONS_NCERT

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Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 3: Find the derivative of x at x = 1. Solution 3: Let f(x) = x. Accordingly, f 1h f 1 f ' 1 lim h0 h 1h 1 lim h0 h h lim h0 h lim 1 h0 = 1 Thus, the derivative of x at x = 1 is 1. Question 4: Find the derivative of the following functions from first principle. 3 x â€“ 27 (ii) (x â€“ 1) (x â€“ 2) (i) 1 x1 (ii) (iv) 2 x x1 Solution 4: 3 (i) Let f(x) = x â€“ 27. Accordingly, from the first principle, f x h f x f ' x lim h0 h 3 3 x h 27 x 27 lim h0 h 3 3 2 2 3 x h 3x h3xh x lim h0 h 3 2 2 h 3x h3xh lim h0 h 3 2 2 lim h 3x h3xh h0 2 2 03x 0 3x (ii) Let f(x) = (x â€“ 1) (x â€“ 2). Accordingly, from the first principle, 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 ______________________________________________________________________________ f ' x lim h0 lim h0 h0 x h 1 x h 2x 1 x 2 2 2 2 x hx 2x hx h 2h x h 2x 2x x 2 f x h f x lim h0 h 2 hx hx h 2h h lim h0 h 2 2hx h 3h lim h0 h lim 2x h3 h 2x 3 1 (iii) Let f(x) = . Accordingly, from the first principle, 2 x f x h f x f ' x lim h0 h 1 1 2 2 x h x lim h0 h 2 2 1 x x h lim h 0 2 2 h x x h 2 2 1 x x h lim h 0 2 2 h x x h 2 2 2 1x x h 2hx lim h 0 2 2 h x x h 2 1h 2hx lim h 0 2 2 h x x h 2 h 2x lim h 0 2 2 x x h 02x 2 2 x x0 x 2 3 (iv) Let f(x) = h x1 . Accordingly, from the first principle, x 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.
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Class XI Chapter 1 - Sets Maths ___
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Class XI Chapter 2 - Relations and
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Class XI Chapter 3 - Trigonometric
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Class XI Chapter 4 - Principle of M
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Class XI Chapter 5 - Complex Number
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Class XI Chapter 6 - Linear Inequal
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Class XI Chapter 7 - Permutation an
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 9 - Sequences and
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Class XI Chapter 10 - Straight Line
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Class XI Chapter 11 - Conic Section
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Page 399 and 400: Class XI Chapter 11 - Conic Section
Page 417 and 418: Class XI Chapter 12 - Introduction
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Page 491 and 492: Class XI Chapter 14 - Mathematical
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Class XI Chapter 14 - Mathematical
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Class XI Chapter 15 - Statistics Ma
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