Home
Class 12
MATHS
If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 a...

If `f(x+y+z)=f(x)+f(y)+f(z)` with `f(1)=1` and `f(2)=2` and `x,y, z epsilonR` the value of `lim_(xtooo)sum_(r=1)^(n)((4r)f(3r))/(n^(3))` is ……….

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

  • TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION - I)|39 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If f(x+y)=f(x)*f(y) and f(1)=4. Find sum_(r=1)^(n)f(r)

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(xy) =(f(x))^(y) + (f(y))^(x) for all x, y in R and f(1) =3 , then the value of sum_(t=1)^(10) f(r) is equal to

If f(x+y)=f(x)+f(y) -xy -1 for all x, y in R and f(1)=1 then f(n)=n, n in N is true if

If f(x)=3^(1+x)," then "f(x)f(y)f(z) is equal to

If sum_(r=1)^(n)r^(4)=F(x), then prove that the value of sum_(n=1)^(n)r(n-r)^(3) is (1)/(4)[n^(3)(n+1)^(2)-4F(x)]

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5, then f(x) is an odd function f(x) is an even function sum_(n=1)^(m)f(r)=5^(m+1)C_(2)sum_(n=1)^(m)f(r)=(5m(m+2))/(3)

If f((x+2y)/(3))=(f(x)+2f(y))/(3)AA x,y in R and f'(0)=1,f(0)=2 then find f(x) .

FIITJEE-TIPS-NUMERICAL BASED QUESTIONS
  1. If alpha is a the absolute maximum value of the expression (3x^(2)+2x-...

    Text Solution

    |

  2. The value of (8sqrt2)/(pi)int(0)^(1)((1-x^(2))/(1+x^(2)))(dx)/(sqrt(1+...

    Text Solution

    |

  3. The value of lim(xrarr0)(16-16 cos (1-cos x))/(x^(4)) is

    Text Solution

    |

  4. The value of lim(xrarrpi//2)12 tan^(2)x[sqrt(6+3 sin x-2cos^(2)x)-sqrt...

    Text Solution

    |

  5. f(x)=sqrt(x-1)+sqrt(2-x)andg(x)=x^(2)+bx+c are two given functions suc...

    Text Solution

    |

  6. If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR ...

    Text Solution

    |

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

    Text Solution

    |

  8. The value of f(0) so that the function f(x)=(1)/(x)-(1)/(sinx) is cont...

    Text Solution

    |

  9. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

    Text Solution

    |

  10. Find the area enclosed by the curves max(|x+y|,|x-y|)=1

    Text Solution

    |

  11. The number of points at which the function, f (x)={{:(min {|x|"," x ...

    Text Solution

    |

  12. f(x)=[x] and g(x)={{:(1",",x gt1),(2",", x le 1):}, (where [.] represe...

    Text Solution

    |

  13. underset(xto1)lim[cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the...

    Text Solution

    |

  14. int(1)^(7)(log sqrt(x))/(log sqrt(8-x)+log sqrt(x))dx=

    Text Solution

    |

  15. Period of function 2^({x})+sin 2pix+3^({x//2)}+cos 2pix, (where {x} de...

    Text Solution

    |

  16. Let y=(a sin x+(b+c)cosx)e^(x+d) where a, b, c, d are parameters. The ...

    Text Solution

    |

  17. lim(n->oo)(n^(alpha)sin^2n !)/(n+1), 0ltalphalt1, is equal to :

    Text Solution

    |

  18. If f(x) ge 0 for all x in [0,10] and int(2)^(8) f(x)=0, then f(7) is

    Text Solution

    |

  19. The area of quadrilateral combined equation of whose sides are (x^(2...

    Text Solution

    |

  20. The number of points of non differentiability of y=|log|x|| are

    Text Solution

    |