Home
Class 12
MATHS
Let f :RtoR be a positive, increasing fu...

Let `f :RtoR` be a positive, increasing function with
`underset(xtooo)lim(f(3x))/(f(x))=1`. Then `underset(xtooo)lim(f(2x))/(f(x))` is equal to

A

`3//2`

B

`3`

C

`1`

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that ` f(x) ` is a positive increasing function.
` therefore 0 lt f(x)lt f(2x)lt f(3x)`
`rArr 0 lt 1 lt(f(2x))/(f(x))lt (f(3x))/(f(x))`
`rArr 1lt (f(2x))/(f(x)) lt (f(3x))/(f(x))`
Clearly, `lim_(xtooo) 1=1 and lim_(xtooo) (f(3x))/(f(x))=1`. Therefore , by Sandwich theorem
` lim_(xto oo)(f(2x))/(f(x))=1`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|96 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

Let f : R to [0,oo)" be such that "underset(x to 5)lim f(x)" exists and "underset(x to 5)lim ([f(x)]^(2)-9)/(sqrt(|x-5|))=0." Then "underset(x to 5)lim f(x) is equal to:

If f(x )=sqrt(25-x^(2)) , then what is underset(xto1)lim(f(x)-f(1))/(x-1) equal to

Let f : R to R be a differentiable function satisfying f'(3) + f'(2) = 0 , Then underset(x to 0) lim ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) is equal to

Let f(2)=4 and f'(2)=4 . Then lim_(x->2)(xf(2)-2f(x))/(x-2) is equal to

If f is derivable at x =a,then underset(xto a ) lim( (xf(a) -af( x))/(x-a) )

lim_(xtooo) (x(logx)^(3))/(1+x+x^(2)) equals

The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-x))dx is equal to

If f (x) is a function such that f(x+y)=f(x)+f(y) and f(1)=7" then "underset(r=1)overset(n)sum f(r) is equal to :

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where underset(x to 0)lim g(x)=1 . Then f'(x) is equal to

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
  1. Find the value of alpha so that ("lim")(xvec0)1/(x^2)(e^(alphax)-e^x-x...

    Text Solution

    |

  2. lim(xrarr0) x^8[(1)/(x^3)], where [.],denotes the greatest integer fun...

    Text Solution

    |

  3. Let f :RtoR be a positive, increasing function with underset(xtooo)l...

    Text Solution

    |

  4. Let f : R to [0,oo)" be such that "underset(x to 5)lim f(x)" exists an...

    Text Solution

    |

  5. Let f(theta)-1/(tan^(2)theta){(1+tan theta)^(3)+(2+tan theta)^(3)+….+(...

    Text Solution

    |

  6. Let f(x)=3x^10-7x^8+5x^6-21x^3+3x^2-7 , then the value of lim(h->0)...

    Text Solution

    |

  7. The largets value of non negative integer for which lim(x->1){(-a x+si...

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. lim(xrarr oo) {3sqrt((x+a)(x+b)(x+c))-x}=

    Text Solution

    |

  10. ("lim")(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n(when alpha in Q) i...

    Text Solution

    |

  11. The value of lim(n->oo) (1^2 . n+2^2.(n-1)+......+n^2 . 1)/(1^3+2^3+....

    Text Solution

    |

  12. lim(nrarr oo) ((nsqrt(a)+nsqrt(b))/(2))^n,a,b,gt 0 equals

    Text Solution

    |

  13. underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x...

    Text Solution

    |

  14. lim(xrarr 1) (x^(2^(32))-2^32x+4^16-1)/((x-1)^2) is equal to

    Text Solution

    |

  15. The value of lim(xrarr oo) (3sqrt(x^3+x^2)-3sqrt(x^3-x^2)), is

    Text Solution

    |

  16. If lim(xrarr-1)(sin(x^3+bx^2+cx +d))/((sqrt(2+x)-1){loge(x+2)}^2) exis...

    Text Solution

    |

  17. If lim(xrarr1)(ax^2+bx+c)/((x-1)^2)=2, then lim(xrarr1)((x-a)(x-b)(x-c...

    Text Solution

    |

  18. The value of lim(xrarr0) (loge(1+x)-x)/(x{(1+x)^(1//x)-e}) equal to

    Text Solution

    |

  19. The value of lim(xrarr0) (sin(sinx)-tan(sinx))/(sin^3(sinx)), is

    Text Solution

    |

  20. The value of lim(xrarr oo) x{(1)/(e)-((x)/(x+1))^x} , is

    Text Solution

    |