Home
Class 12
MATHS
Let f(x) = {(x sin(1/x)+sin(1/x^2),; x!=...

Let `f(x) = {(x sin(1/x)+sin(1/x^2),; x!=0), (0,;x=0):},` then `lim_(x rarr oo)f(x)` is equal to

A

0

B

`-1//2`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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,x 0 then lim_(x rarr0)f(x) is equal to

lim_(x rarr0)sin^(-1)(sec x) is equal to

Let f(x)=det[[cos x,x,x2sin x,x,2xsin x,x,x]], then lim_(x rarr0)(f(x))/(x^(2)) is equal to (a)0(b)-1(c)2(d)3

if f(x)={((1)/(x))sin x,x!=0,0,x=0}f in d lim_(x rarr0)((1)/(x))sin x

Let (x)=|[cos x,2sin x,sin x],[x,x,x],[1,2x,x]|," then "lim_(x rarr0)(f(x))/(x^(2) is equal

f(x)=e^x then lim_(x rarr 0) f(f(x))^(1/{f(x)} is

lim_(x rarr0)((1)/(x))^(sin x)

If f(x)=int((2sin x-sin2x)/(x^(3))dx);x!=0 then lim_(x rarr0)f'(x) is: (A) 0(B)oo(C)-1 (D) 1

let f(x)=det[[cos x,x,12sin x,x^(2),2xtan x,x,1]]. then lim_(x rarr0)(f'(x))/(x)=

Consider the function f(x)={(max(x,(1)/(x)))/(min(x,(1)/(x))),quad if x!=0 and 1,quad if x=0 then lim_(x rarr0){f(x)}+lim_(x rarr1){f(x)},lim_(x rarr1)[f(x)]=

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Solved Examples Level 1 (Single Correct Answer)
  1. Let f : R to [0,oo)" be such that "underset(x to 5)lim f(x)" exists an...

    Text Solution

    |

  2. If f(x)={((sin(1+[x]))/([x])"for"[x] ne 0,),(0" for " [x]-0,):} where ...

    Text Solution

    |

  3. Let f(x) = {(x sin(1/x)+sin(1/x^2),; x!=0), (0,;x=0):}, then lim(x rar...

    Text Solution

    |

  4. which of the following limits equal to 1/2 : (A) lim(n->oo)(1/1.3+...

    Text Solution

    |

  5. If lim(x to 0) (1+ax)^(b//x)=e^4 , where a and b are natural numbers t...

    Text Solution

    |

  6. lim(xto0)(a^x-1)/(sqrt(a+x)-sqrta) is

    Text Solution

    |

  7. f(x) = 3x^10 – 7x^8+ 5x^6 -21x^3 + 3x^2 –7, then is the value of lim(...

    Text Solution

    |

  8. lim(x rarr0)(e^(x^(2))-cos x)/(x^(2))" is equal to " (a) 3/2 (b) 1/...

    Text Solution

    |

  9. Let f(x)=ltxgt^(**), where lt xgt^(**) is the distance from x to the i...

    Text Solution

    |

  10. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

    Text Solution

    |

  11. lim(xto0)(sin(picos^(2)x))/(x^(2)) is equal to

    Text Solution

    |

  12. Let f(x)=sgn (sgn (sgn x)). Then lim(x to0) f(x) is

    Text Solution

    |

  13. lim(x->a-) {(|x|^3)/a-[x/a]^3} ,(a < 0), where [x] denotes the greates...

    Text Solution

    |

  14. lim(x to 0){(1+tanx)/(1+sinx)}^("cosec x") is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |