NCERT class 11 maths chapter 13 Limits and Derivatives
Question 1:Find the derivative of x2 – 2 at x = 10.
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Question 2:Find the derivative of x at x = 1.
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Question 3:Find the derivative of 99x at x = l00.
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Question 4:Find the derivative of the following functions from first principle. (i) 3 x − 27 (ii) (x −1)(x − 2) (iii) 2 1 x (iv) 1 1 x x + −
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Question 5:For the function ( ) 100 99 2 . . . 1 100 99 2 x x x f x = + + + + x + . Prove that f (1) =100 f (0).
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Question 6:Find the derivative of 1 2 2 1 . . . n n n n n x ax a x a x a + − + − + + − + for some fixed real number a.
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Question 7:For some constants a and b, find the derivative of (i) (x − a) (x − b) (ii) ( )2 2 ax + b (iii) x a x b − −
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Question 8:Find the derivative of n n x a x a − − for some constant a.
EXERCISE 13.21. Find the derivative of x2 2 at x
Question 9:Find the derivative of (i) 3 2 4 x − (ii) ( ) ( ) 35x + 3x −1 x −1 (iii) 3 ( ) x 5 3x − + (iv) 5 ( 9 ) x 3 6x− − (v) 4 ( 5 ) x 3 4x − − − (vi) 2 2 1 3 1 x x x − + −
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Question 10:Find the derivative of cos x from first principle.
Question 11:Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5sec x + 4cos x (iv) cosec x (v) 3cot x + 5cosec x (vi) 5sin x − 6cos x + 7 (vii) 2tan x − 7sec x
