EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>Exercise 1>Q 53

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IMPORTANT

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$If \log_{e} y = 3 \sin^{- 1} x, then (1 - x)^{2} y " - xy at x = \frac{1}{2} is equal to :$

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Important Questions on Differential Coefficient

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>Exercise 1>Q 54

Let f (x) be a real differentiable function such that f (0) = 1 and f (x + y) = f (x) ƒ' (y) + f' (x) f (y) for all x, y \in R . Then \sum_{n = 1}^{100} \log_{e} f (n) is equal to :

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>Exercise 1>Q 55

Let

f : (0, \infty) \to R

be a function which is differentiable at all points of its domain and satisfies the condition

x^{2} f' (x) = 2 x f (x) + 3

, with

f (1) = 4

. Then

2 f (2)

is equal to:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Differential Coefficient>Exercise 1>Q 56

Let f be a real valued continuous function defined on the positive real axis such that g (x) = \int_{0}^{x} tf (t) dt . If g (x^{3}) = x^{6} + x^{7}, then value of \sum_{r = 1}^{15} f (r^{3}) is :