Home
Class 12
MATHS
f(x)+f(y)=f((x+y)/(1-x y)) for allx ,y ...

`f(x)+f(y)=f((x+y)/(1-x y))` for all`x ,y in Rdot` `(x y!=1)`,and `lim_(xto0)(f(x))/x=2`.Find `f(1/(sqrt(3)))a n df^(prime)(1)dot`

A

`2 tan^(-1)x`

B

`(1)/(2) tan^(-1)x`

C

`(pi)/(2) tan^(-1)x`

D

`2 pi tan^(-1) x`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 6|5 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f((x)/(y))=(f(x))/(f(y)) forall x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4 . Then, f(5) is

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1 , then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f'(1)=1, then f(e) is.

If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim_(xto oo)f(x) is

If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N such that f(1)=3 and sum_(x=1)^nf(x)=120 , find the value of n .

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Domain of log(f(x)), is

if f: 9R to 9R satisfies f(x+y)=f(x)+f(y) , for all x, y , in 9 R and f(1)=10 then sum_(r=1)^(n) f(r)

If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5, then find sum_(n=1)^(m)f(n) . Also, prove that f(x) is odd.