Home
Class 12
MATHS
Let f : R to R be a function such that ...

Let ` f : R to R` be a function such that
`f(x+y) = f(x)+f(y),Aax, y in R.` If f (x) is differentiable at x = 0, then

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos

  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in R If f(x) is differentiable at x=0. then, which one of the following is incorrect?

Let f:R rarr R be a function such that f(x+y)=f(x)+f(y),AA x,y in R

Let f(x+y)=f(x)+f(y)AA x, y in R If f(x) is continous at x = 0, then f(x) is continuous at

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f : R to R be a function given by f(x+y)=f(x)f(y) for all x , y in R If f(x) ne 0 for all x in R and f'(0) exists, then f'(x) equals

Let f:R rarr R be a function such that f((x+y)/(3))=(f(x)+f(y))/(3),f(0)=0 and f'(0)=3

Let f:R rarr R be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f: Rvec be such that f(!)=3a n df^(prime)(1)=6. Then ("lim")(xvec...

    Text Solution

    |

  2. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

    Text Solution

    |

  3. If (lim)(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the val...

    Text Solution

    |

  4. If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...

    Text Solution

    |

  5. The function given by y=||x|-1| is differentiable for all real n...

    Text Solution

    |

  6. If |f(x1) - f(x2)| le (x1 - x2)^(2), AA x1 , x2 in R. Find the equatio...

    Text Solution

    |

  7. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  8. If lim(x-&gt;0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b &gt;0,where theta...

    Text Solution

    |

  9. If f(x) {-x-pi/2,xle-pi/2 and -cosx,-pi/2 < xle0 and x-1,0< x le1 and ...

    Text Solution

    |

  10. Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in...

    Text Solution

    |

  11. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

    Text Solution

    |

  12. Let f(x)={x^2|cospi/x|,\ x!=0 ,\ x=0,\ x in Rdot\ t h e n\ f is (a) D...

    Text Solution

    |

  13. If ("lim")(xvecoo)((x^2+x+1)/(x+1)-a x-b)=4,t h e n a=1,b=4 (b) a=1,...

    Text Solution

    |

  14. Evaluate: ("lim")(xvec0)(log(5x)-"log"(5-x))/x

    Text Solution

    |

  15. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  16. Let F(x) ={(x-1)sin1/(x-1) , x!=1 ,{ 0, x=1 then which one of the f...

    Text Solution

    |

  17. Let f(x)""=""x|x|""a n d""g(x)""=""s in x Statement 1 : gof is diff...

    Text Solution

    |

  18. (lim)(xvec2)((sqrt(1-cos{2(x-2)}))/(x-2)) (1) does not exist (2) equa...

    Text Solution

    |

  19. The value of p and q for which the function f(x)""={(sin(p+1)x+sinx)/x...

    Text Solution

    |

  20. (lim)(xvec0)((1-cos2x)(3+cosx)/(xtan4x) is equal to: (1) 4 (2) 3 (...

    Text Solution

    |