Home
Class 12
MATHS
If f(x) be differentiable function and c...

If `f(x)` be differentiable function and curve `y=f(x)` passes through (1, 1) and satisfies the relation `2f(x+y)+f(x-y)+3y^2` then `=3f(x)+2xy`, `lim_(x to 1)(f(x)-1)/(x-1)` is equal to

A

3

B

0

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • NTA TPC JEE MAIN TEST 66

    NTA MOCK TESTS|Exercise MATHEMATICS|30 Videos

  • NTA TPC JEE MAIN TEST 68

    NTA MOCK TESTS|Exercise MATHEMATICS|29 Videos

Similar Questions

Explore conceptually related problems

If the curve y=f(x) passes through the point (1, -1) and satisfies the differential equation : y(1+xy)dx=x dy , then f(- 1/2) is equal to :

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

If the function f(x) satisfies the relation f(x+y)=y(|x-1|)/((x-1))f(x)+f(y) with f(1)=2. then lim_(x rarr1)f'(x) is

If the function f(x) satisfies lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi , then lim_(x to 1)f(x) is equal to

If f(x) be a differentiable function for all positive numbers such that f(x.y)=f(x)+f(y) and f(e)=1 then lim_(x rarr0)(f(x+1))/(2x)

Suppose a differntiable function f(x) satisfies the identity f(x+y)=f(x)+f(y)+xy^(2)+xy for all real x and y .If lim_(x rarr0)(f(x))/(x)=1 then f'(3) is equal to

NTA MOCK TESTS-NTA TPC JEE MAIN TEST 67-MATHEMATICS
  1. Given abs(veca)-abs(vecb)=1 and abs(veca+vecb)=sqrt3, "if" vec c be a ...

    Text Solution

    |

  2. let where a, b, c are real constants and f(x)=lim(n to oo)g(x). If ...

    Text Solution

    |

  3. If f(x) be differentiable function and curve y=f(x) passes through (1,...

    Text Solution

    |

  4. If 2ysinx(dy)/(dx)=sin2x-y^2 cosx and at x=pi/2,y=1, then

    Text Solution

    |

  5. If int((x^2-x+1)/(x^2+1)).e^(cot^(-1)x)dx=A(x).e^(cot^-1x)+C, where C ...

    Text Solution

    |

  6. The value of x in (0, pi/2) satisfying equation (sqrt5-1)/(sinx)+sqrt(...

    Text Solution

    |

  7. Rectangle ABCD has area 200 sq. unit. An ellipse with area 200 pi. uni...

    Text Solution

    |

  8. Number of solutions of the equations y=1/3[sinx+[sin x + [sin x]]] and...

    Text Solution

    |

  9. If sin^(-1)(2a)/(1+a^2)+sin^-1""(2b)/(1+b^2) then x is =2 ta^-1 x, e...

    Text Solution

    |

  10. If the line 2x+y+k=0 is a mormal to the parabola y^2+8x=0, then the va...

    Text Solution

    |

  11. The coefficient of variation of 10 observations, if the sum of squares...

    Text Solution

    |

  12. The logical proposition (~(~p vv q) vv (p ^^ r)) ^^ (~q ^^ r) is equic...

    Text Solution

    |

  13. The area enclosed by y=g(x)," "x=-3," "x=5 and x-axis where g(x) is th...

    Text Solution

    |

  14. The expansion of (1+x+x^2)^n is a0+a1x+a(2)x^(2)+ … +a(2n)x^(2n). Find...

    Text Solution

    |

  15. If {:[((-1+isqrt3)/(2i),(-1,isqrt3)/(2i)),((i+isqrt3)/(2i),(1 - isqrt3...

    Text Solution

    |

  16. For the quadratic equation 6x^2+11x+3=0, if alpha and beta are the roo...

    Text Solution

    |

  17. if 5f(x)+3f(1/x)=x+2 and y=x f(x), then ((dy)/(dx))(x=1) is equal

    Text Solution

    |

  18. Find the length of PQ such that the tangent at the point P on the circ...

    Text Solution

    |

  19. A 2 xx 2 matrix is fromed with entries from the set {0, 1}, The probab...

    Text Solution

    |

  20. Let f be a function defined on R such that f^'(x)=2018(x-2017)(x-201...

    Text Solution

    |