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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(4)= 4, f'(4) =1 then lim_(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is equal to

If f(x) = ax^2+bx+c and f(1)=3 and f(-1)=3, then a+c equals

If f (x) = x^(4) + 2x^(3) , them lim_(x to 2) (f(x) - f(2))/(x - 2) is equal to

If f(x) is derivable at x=2 such that f(2)=2 and f'(2)=4 , then the value of lim_(h rarr0)(1)/(h^(2))(ln f(2+h^(2))-ln f(2-h^(2))) is equal to

The value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

If f'(x)=(1)/((1+x^(2))^(3//2)) and f(0)=0, then f(1) is equal to :

If a function F is such that F(0)=2 , F(1)=3 , F(n+2)=2F(n)-F(n+1) for n ge 0 , then F(5) is equal to

If f(1)=2, f\'(x)=f(x) and h(x)=fof(x) then h'\(1) is equal to (A) 4e (B) 2e^2 (C) 4e^2 (D) e^2

If f(x)=cos^(-1)(4x^3-3x)and lim_(xto1/2+)f'(x)=a and lim_(xto1/2-)f'(x)=b then a + b+ 3 is equal to ____

If f'(x)=(dx)/((1+x^(2))^(3//2)) and f(0)=0. then f(1) is equal to

CENGAGE ENGLISH-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)(hvec0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h

    Text Solution

    |

  5. If x^2+y^2=1,t h e n (a)y y^('')-2(y^(prime))^2+1=0 (b)yy^('')+(...

    Text Solution

    |

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

    Text Solution

    |

  7. If y is a function of x and log(x+y)-2x y=0, then the value of y^(prim...

    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)) using the first principle...

    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)) the...

    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|, then f'(x) equals

    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, and h are differentiable functions of x and (delta)=|[f,g,h]...

    Text Solution

    |

  20. Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x...

    Text Solution

    |