Home
Class 11
MATHS
If f(x)=cos(logx),show that f(x)f(y)-1/2...

If `f(x)=cos(logx)`,show that `f(x)f(y)-1/2`[`f``(x/y)`+`f(xy)`]=0

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 6

    UNITED BOOK HOUSE|Exercise EXERCISE|47 Videos
  • MODEL QUESTION PAPERS-SET 8

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

Similar Questions

Explore conceptually related problems

If f(x) = cos (log _(e) x), then f (x) f(y) -1/2 [f(xy) +f((x)/(y))] has the value-

If f(x) = cos(log x) then f(x)f(y)-1/2[f(x/y)+f(xy)] has the value

Given f(x)=cos (logx), find the value of f(x).f(y)-(1)/(2)[f(x/y)+f(xy)]

If , f(x)="log"((1+x)/(1-x)) ,show that f(x)+f(y)=f((x+y)/(1+xy))

If f(x) = (x-1)/(x+1) , then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy) .

If f(x) = cos(log_e x) , then find the value of f(x) cdot f(y) - 1/2[f(x/y) + f(xy)]

If f (x) = sin (log x) then the value of f(xy)+f((x)/(y))-2f (x) cos (log y) is-

If f'(x)=logx and f(1)=0, show f(x)=x(logx-1)+1.

A function f (x) is defined for all x in R and satisfies, f(x + y) = f (x) + 2y^2 + kxy AA x, y in R , where k is a given constant. If f(1) = 2 and f(2) = 8 , find f(x) and show that f (x+y).f(1/(x+y))=k,x+y != 0 .

If f'(x)=sin(logx) and y=f((2x+3)/(3-2x)) , find (dy)/(dx) .

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 7-EXERCISE
  1. 4 cards are drawn from a well - shuffled deck of 52 cards. What is the...

    Text Solution

    |

  2. If the variance of a distribution is 4 coefficient of variation is 5%,...

    Text Solution

    |

  3. If f(x)=cos(logx),show that f(x)f(y)-1/2[f(x/y)+f(xy)]=0

    Text Solution

    |

  4. Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(s...

    Text Solution

    |

  5. Solve : sectheta-1=(sqrt2-1)tantheta

    Text Solution

    |

  6. By mathematical induction show that 3^n>n^3when nge4. N is an integer.

    Text Solution

    |

  7. Find the co-efficient of 1/xof the expansion of (1+x)^n(1+1/x)^nwhere ...

    Text Solution

    |

  8. Find the sum up to n terms :n.1+(n-1).2+(n-2)3+(n-3).4+....

    Text Solution

    |

  9. If n(p(r-1))/a=n(pr)/b=n(p(r+1))/c,then show that b^2=a(b+c)

    Text Solution

    |

  10. Show that the four lines 2x+y+1=0,2x+y+7=0,x+2y-1=0 and x+2y+5=0 form ...

    Text Solution

    |

  11. Find the equation-of the bisector of the obtused angle between the st...

    Text Solution

    |

  12. The co-ordinate of centre and the diameter of a circle are (3, 7) and ...

    Text Solution

    |

  13. Find the ratio in which the YZ. plane divides the line segment joining...

    Text Solution

    |

  14. Evaluate :lim(xrarr0)(sqrtcosx-root(3)(cosx))/(sin^2x)

    Text Solution

    |

  15. Find, form 1st principles, the derivatives of tansqrtxwith respect to ...

    Text Solution

    |

  16. Using contrapositive method show that the following statement is true....

    Text Solution

    |

  17. Find the validity of the following biconditional Statement. A triangle...

    Text Solution

    |

  18. For any three events A. B.' C show thatP(AcupBcupC)=P(A)+P(B)+P(C)-P(A...

    Text Solution

    |

  19. The mean and SD of the scoreing marks of 100 students are 40 and 5.1 r...

    Text Solution

    |

  20. if tan (beta/2)=4 tan (alpha/2),show that tan( (beta-alpha)/2)=(3sinal...

    Text Solution

    |