Home
Class 12
MATHS
If f be a function such that f(9) = 9 an...

If f be a function such that f(9) = 9 and f'(9) = 3, then :
`lim_(x rarr 9) (sqrt(f(x)) - 3)/(sqrt(x) - 3)` is :

A

1

B

9

C

3

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

If f(9) =9, f^(')(9) = 4 , then lim_(x rarr 9)(sqrt(f(x))-3)/(sqrtx - 3) =

If f(1) =1 and f^(')(1) =2 then lim_(x rarr 1) (sqrt(f(x))-1)/(sqrt(x) -1) =

lim_(x rarr 0) (sqrt(2+x^(3)) - sqrt(2-x^(3)))/ x^(3) =

If f(2) = 4 and f^(')(2) =1 then lim_(x rarr 2) (x f(2)-2f (x))/(x-2)

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

If g(x) = 1/sqrt(9+x^(2) then lim_(x rarr 4) ((g(x) - g(4))/(x-4) =

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(x rarr oo) [sqrt(x+sqrt(x + sqrt (x-)) sqrtx]=

    Text Solution

    |

  2. lim(x rarr 1) (log(e)x)/(x-1) equals :

    Text Solution

    |

  3. If f be a function such that f(9) = 9 and f'(9) = 3, then : lim(x ra...

    Text Solution

    |

  4. lim(x rarr 0) ((1^(x)+2^(x)+3^(x)+……….+n^(x))/n)^(1/x) =

    Text Solution

    |

  5. If f(x) = (sin (e^(x-2) - 1))/(log (x - 1)), then lim(x rarr 2) f(x) i...

    Text Solution

    |

  6. lim(x rarr 0) ((tan x -x)/x). (Sin) 1/x =

    Text Solution

    |

  7. If lim(x rarr 0) (x(1+m cos x)-n(sin x))/x^(3) =1 then

    Text Solution

    |

  8. lim(x rarr 0) (cos x + a sin bx)^(1/x) =

    Text Solution

    |

  9. lim(x rarr a) (x^(7/6)-a^(7/6))/(x^(3/5)-a^(3/5)), (a gt 0) =

    Text Solution

    |

  10. lim(n rarr oo) [1/(1-n^(4))+ 8/(1-n^(4))+ ....+ n^(3)/(1-n^(4)]] =

    Text Solution

    |

  11. lim(n rarr oo) [2/3 + (2/3)^(2) + (2/3)^(2)+.....+(2/3)^(n)] =

    Text Solution

    |

  12. lim(n rarr oo) (1)/(n^(3)) sum(r = 1)^(n) r^(2) is :

    Text Solution

    |

  13. lim(x rarr oo) (1)/(n^(4)) sum(r = 1)^(n) r^(3) is :

    Text Solution

    |

  14. lim(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) ...

    Text Solution

    |

  15. lim(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n+1))/2} =

    Text Solution

    |

  16. If S(n) = (1)/(1.4)+(1)/(4.7) + (1)/(7.10) +……. to n terms, then lim(n...

    Text Solution

    |

  17. lim(x rarr 1) (x^(2)-1)/(|x-1|) =

    Text Solution

    |

  18. If f(x) = {(1/(1+e^(1/x)), x ne 0),(0, x= 0):} then f(x) is

    Text Solution

    |

  19. The right hand and left hand limit of the function f(x)={{:((e^(1//x)-...

    Text Solution

    |

  20. Let f(x) = {(x", if x is irrational"),(0", if x is ratinal"):} then f ...

    Text Solution

    |