﻿ Give a function g which has derivative g’(x) for all x satisfying g’(0) = 2 and g(x + y) = ey g(x) + ex g(y) for all x, y Ïµ R, g(5) = 32. The value ofg’(5) – 2e5 is : Kaysons Education

# Give A Function g which Has Derivative g’(x) For All x satisfying g’(0) = 2 And g(x + y) = ey g(x) + ex g(y) For All x, y Ïµ R, g(5) = 32. The Value Ofg’(5) – 2e5 is

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

32

Putting x = y = 0 in g(x + y) = ey g(x) + ex g(y)

We get g(0) = g(0) + g(0) = 2g(0) ⇒ g(0) = 0

#### SIMILAR QUESTIONS

Q1

The derivatives of sec –1 [1/(2x2 – 1)] with respect to  at x = ½, is

Q2

Let F(x) = f(xg(xh(x) for all real x, where f(x), g(x) and h(x) are differentiable functions. At some point x0,

Q3

If the function  then the value ofg’(1) is

Q5
Q6

The function y = (x2 + 1)50 is differentiated 70 times to get y70(x). Theny70(x) is a polynomial of degree is equal to

Q7

Let f(x + y) = f(xf(y) for all xy Ïµ R and suppose that is differentiable at 0 and f’(0) = 4. If f(x0) = 8 then f’(x0) is equal to

Q8

A function f (x) is defined for x > 0 and satisfies f(x2) = x3 for all x > 0. Then the value of f’(4) is

Q9

Let P(x) be a polynomial of degree 4, with (2) = –1, P’ (2) = 0, P’’ (2), P’’’ (2) = –12 and Piv(2) = 24. The value of P’’(1) is