Amit M Agarwal Solutions for Chapter: Continuity and Differentiability, Exercise 4: Target Exercise 6.4

Author:Amit M Agarwal

Amit M Agarwal Mathematics Solutions for Exercise - Amit M Agarwal Solutions for Chapter: Continuity and Differentiability, Exercise 4: Target Exercise 6.4

Attempt the practice questions on Chapter 6: Continuity and Differentiability, Exercise 4: Target Exercise 6.4 with hints and solutions to strengthen your understanding. Skills in Mathematics Differential Calculus for JEE Main & Advanced solutions are prepared by Experienced Embibe Experts.

Questions from Amit M Agarwal Solutions for Chapter: Continuity and Differentiability, Exercise 4: Target Exercise 6.4 with Hints & Solutions

HARD
JEE Main
IMPORTANT

If f(x)=1-4x20≤x≤1x2-2x1≤x<2(where .) denotes the greatest integer function). Then:

HARD
JEE Main
IMPORTANT

Let f(x) be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=2x2+3x.g(x) for all x, where gx is continuous and g(0)=3. Then, f'(x) is equal to

HARD
JEE Main
IMPORTANT

Given a function g(x) which has derivates g'(x) for every real x and which satisfies the equation gx+y=eygx+exgy for all x and y and g'(0)=2, then the value of g'(x)-g(x) is equal to

HARD
JEE Main
IMPORTANT

Let f:R→R be a function satisfying fxy2=fxfy2,∀x,y∈R and  f(1)=f'(1)≠0 Then, fx+f1-x is (for all non zero real values of x):

MEDIUM
JEE Main
IMPORTANT

Let, f:R→-Ï€,Ï€, be a differentiable function such that fx+fy=fx+y1-xy, when xy≠1. If f1=Ï€2 and limx→0f(x)x=2. Then, fx is equal to

MEDIUM
JEE Main
IMPORTANT

Let, fx be a derivable function at x=0  and  fx+yK=fx+fyK K∈R, K≠0,2. Then, fx is

HARD
JEE Main
IMPORTANT

Let, fx=sinx and gx=max{f(t),0≤t≤x , 0≤x≤π}1-cosx2,x>Ï€ . Then gx is