Home
Class 11
MATHS
lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)...

`lim_(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1))` given that `f'(2)=6 and f'(1)=4` then (a) limit does not exist (b) is equal to `- 3/2` (c) is equal to `3/2` (d) is equal to 3

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Let f(2) =4and f '(2) =4, then lim _(xto2)(x f(2) -2f(x))/(x-2) is equal to-

If f'(2)=1 , then lim_(h to 0)(f(2+h)-f(2-h))/(2h) is equal to

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x) is (A) exists and equals to 4 (B) does not exist (C) exists and equals to 0 (D) exists and equals 4//7 .

If |f(x)-f(y)|le2|x-y|^((3)/(2)) AAx,yinR and f(0)=1 then value of int_(0)^(1)f^2(x)dx is equal to (a) 1 (b) 2 (c) sqrt2 (d) 4

If f (x) is differentiable and f'(4) =5, then the vlaue of lim_(xto2) (f(4) -f(x^(2)))/(x-2) is equal to-

Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(1) = 2 Answer the following question based on above passage : f'(3) is equal to

Suppose f (x) is differentiable at x=1 and lim _(h to0) (f(1+h))/(h) =5. Then f '(1) is equal to-

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If f(x) is differentiable and strictly increasing function, then the v...

    Text Solution

    |

  2. If f(x)=[2x]sin3pix then prove that f'(k^(+))=6kpi(-1)^(k), (where [.]...

    Text Solution

    |

  3. lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and ...

    Text Solution

    |

  4. Evaluate lim(h->0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h

    Text Solution

    |

  5. If x^2+y^2=1, then (a)y y^('')-2(y^(prime))^2+1=0 (b)yy^('')+(y...

    Text Solution

    |

  6. Using the first principle, prove that d/(dx)(1-x^2)=-2x

    Text Solution

    |

  7. If y is function of x and log(x+y)=2xy, then find the value of y'(0).

    Text Solution

    |

  8. Find the derivative of sqrt(4-x) w.r.t. x using the first principle.

    Text Solution

    |

  9. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  10. If f(x)=xtan^(-1)x , find f^(prime)(sqrt(3)) .

    Text Solution

    |

  11. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

    Text Solution

    |

  12. Find the derivative of e^(sqrt(x)) w.r.t. x using the first principle.

    Text Solution

    |

  13. f(x)=tan^(-1){log(e/x^2)/log(ex^2)}+tan^(-1)((3+2logx)/(1-6logx)) then...

    Text Solution

    |

  14. If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, ...

    Text Solution

    |

  15. If f(x)=|x^2-5x+6|,t h e nf^(prime)(x)e q u a l s 2x-5for2<x<3 5-2xf...

    Text Solution

    |

  16. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  17. Let f(x^m y^n)=mf(x)+nf(y) for all x , y in R^+ and for all m ,n in ...

    Text Solution

    |

  18. Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AA...

    Text Solution

    |

  19. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

    Text Solution

    |

  20. Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(...

    Text Solution

    |