Home
Class 12
MATHS
If f(x)=((x^2+5x+3)/(x^2+x+2))^x then li...

If `f(x)=((x^2+5x+3)/(x^2+x+2))^x` then `lim_(xtooo)f(x)` is equal to

A

`e^(-4)`

B

`e^3`

C

`e^2`

D

`e^4`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples Level 2 (Single Correct Answer)|30 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Numberical Answer)|16 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Single Correct Answer)|10 Videos

  • JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )

    MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim_(xrarroo)f(x) is equal to

If f(x)=sqrt((x-sinx)/(x+cos^(2)x)),"then "lim_(xtooo) 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)={{:(2+x,xge0),(2-x,xlt0):} then lim_(x to 0) f(f(x)) is equal to

If f(x)=|{:(x,sinx,cosx),(x^2,tanx,x^3),(2x,sin2x,5x):}| then lim_(x to 0)(f'(x))/x is equal to

Consider the function f(x)=((ax+1)/(bx+2))^(x) , where a,bgt0 , the lim_(xtooo)f(x) is

If a differentiable function f(x) satisfies lim_(x to -1) (f(x) +1)/(x^(2)-1)=(3)/(2) Then what is lim_(x to -1) f(x) equal to ?

If f(x)=|x^(2)-5x+6| then f'(x) is equal to

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Solved Examples Level 1 (Single Correct Answer)
  1. lim(x to 0){(1+tanx)/(1+sinx)}^("cosec x") is equal to

    Text Solution

    |

  2. lim(n->oo) (6^n+5^n)^(1/n) is equal to -

    Text Solution

    |

  3. If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xtooo)f(x) is equal to

    Text Solution

    |

  4. underset(xtooo)lim[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

    Text Solution

    |

  5. If (lim)(x->-a)(x^9+a^9)/(x+a)9,\ find the real value of adot

    Text Solution

    |

  6. Let f(x)=[x]+[-x], where [x] denotes the greastest integer less than o...

    Text Solution

    |

  7. Let f(x) be a continuous function defined for 1 <= x <= 3. If f(x) tak...

    Text Solution

    |

  8. Let f(x)= {{:(|x| cos (1//x)+9x^2, xne 0),(k, x=0):} then f is cont...

    Text Solution

    |

  9. If f(x)=tan (pi//4 -x)//cot2x for x ne pi//4. The value of f(pi//4) so...

    Text Solution

    |

  10. Let a function f be defined by f(x)="x-|x|"/x for x ne 0 and f(0)=2. T...

    Text Solution

    |

  11. If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) an...

    Text Solution

    |

  12. The function f(x) = (x-1)^(1/((2-x)) is not defined at x = 2. The valu...

    Text Solution

    |

  13. Let f(x)=(x+x^2+.....+x^n-n)/(x-1), x!=1, then value of f(1) so that f...

    Text Solution

    |

  14. If f(u) = 1/(u^(2)+u-2) , where u = 1/(x-1) , then the points of dis...

    Text Solution

    |

  15. Let f(x) and phi(x) be defined by f(x)=[x] and phi(x)={0, x in I and...

    Text Solution

    |

  16. If a,b are chosen from {1,2,3,4,5,6,7} randomly with replacement. The ...

    Text Solution

    |

  17. The value of lim(xto pi//2)(cot x-cosx)/(pi-2x)^3 is

    Text Solution

    |

  18. If underset(x to 0)lim({(a-n)nx - tan x} sin nx)/x^(2) = 0, where n is...

    Text Solution

    |

  19. Find derivative of tan3x by first principle

    Text Solution

    |

  20. The value of lim(x to 0) (e^(nx)-(1+nx+n^2/2x^2))/x^3 (n gt 0) is

    Text Solution

    |