Home
Class 12
MATHS
Let u(x) and v(x) be differentiable func...

Let `u(x) and v(x)` be differentiable functions such that `(u(x))/(v(x))= 7.` If (u'(x)/(v'(x))= p and ((u'(x))/(v'(x)))' = q,` then `(p+q)/(p-q)` has the value of to `(a) `1` (b) `0` (c) `7` (d) `-7`

A

1

B

0

C

7

D

-7

Text Solution

Verified by Experts

`u(x)=7v(x) or u' (x)=7 v'(x) or p=7" (given)"`
`"Again "(u(x))/(v(x))=7or ((u(x))/(v(x)))=0 or q =0`
`"Now, "(p+q)/(p-q)=(7+0)/(7-0)=1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If (x+iy)^(3)= u +iv , then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2)) .

If P = (x^(2) -36)/(x^(2) -49) and Q= (x+6)/(x+7) find the value of (P)/(Q)

The integrating factor of the differential equation (dy)/(dx)+P(x)y=Q(x) is x, then P(x)

If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.

If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (del u)/(del y)=

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is

If u = tan^(-1)"" (sqrt ( 1+x^2)-1)/(x) and v = tan^(-1) x , find (du)/(dv)

int((x^2+1))/((x+1)^2)dxi se q u a lto ((x-1)/(x+1))e^x+c (b) e^x((x+1)/(x-1))+c e^x(x+1)(x-1)+c (d) none of these

Evaluate: int(dx)/((x-p)sqrt((x-p)(x-q)))

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

    Text Solution

    |

  2. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se...

    Text Solution

    |

  3. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  4. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/...

    Text Solution

    |

  5. Let h(x) be differentiable for all x and let f(x) = (kx=e^(x)) h(x) wh...

    Text Solution

    |

  6. If ("lim")(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, the...

    Text Solution

    |

  7. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |

  8. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (sqrt(pi)...

    Text Solution

    |

  9. d/(dx)cos^(-1)sqrt(cosx)i se q u a lto 1/2sqrt(1+s e cx) (b) sqrt(1+s...

    Text Solution

    |

  10. If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is 1 (b) 2 (c...

    Text Solution

    |

  11. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

    Text Solution

    |

  12. If y=(log)(sinx)(tanx),t h e n(((dy)/(dx)))(pi/4)i se q u a lto 4/(lo...

    Text Solution

    |

  13. int sqrt((1 - x)/(1 + x )) dx is

    Text Solution

    |

  14. The differential coefficient of f((log)e x) with respect to x , where ...

    Text Solution

    |

  15. If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 ...

    Text Solution

    |

  16. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  17. A function f, defined for all positive real numbers, satisfies the equ...

    Text Solution

    |

  18. Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')...

    Text Solution

    |

  19. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  20. If f(x)=x+tanxa n df is the inverse of g, then g^(prime)(x) equals 1/(...

    Text Solution

    |