Home
Class 12
MATHS
If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)g...

If `f(x)=1/3(f(x+1)+5/(f(x+2)))` and `f(x)gt0,AA x epsilonR,` then `lim_(xto oo)f(x)` is

A

`sqrt((2)/(5))`

B

`sqrt((5)/(2))`

C

`oo`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `lim_(xto oo) f(x)=l`, then,
Now, `f(x)=91)/(3){f(x+1)+(5)/(f(x+2))}`
`rArr lim_(xto oo) f(x)=(1)/(3){lim_(xto oo) f(x+1)+(5)/(lim_(xto oo) f(x+2))}`
`rArr l=(1)/(3)(l+(5)/(l))`
` rArr 3l^2=l^2+5rArr 2l^2=5rArr l=sqrt((5)/(2))`.
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

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is

If lim_(xtooo) f(x) exists and is finite and nonzero and if lim_(xtooo) {f(x)+(3f(x)-1)/(f^(2)(x))}=3 , then the value of lim_(xtooo) f(x)" is " _______.

If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR the value of lim_(xtooo)sum_(r=1)^(n)((4r)f(3r))/(n^(3)) is ……….

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

Statement 1: If f(x)=2/(pi) cot^(-1)((3x^(2)+1)/((x-1)(x-2))) , then lim_(xto1^(-))f(x)=0 and lim_(xto2^(-))f(x)=2 Statement 2: lim_(xtooo)cot^(-1)x=0 and lim_(xto -oo)cot^(-1)x=pi

Suppose a function f(x) satisfies the following conditions f (x+y) =(f(x) +f(y))/(f +f(x) f(y))' AA x , y in R and f '(0)=1 Also -1lt f (x) lt 1, AA x in R The value of the limit l t_(xto oo) (f(x))^(x) is:

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt 0 AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is: (a) 1 (b) 2 (c) 3 (d) 4

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
  1. lim(xrarr0+) (sinsqrt(x))/(sqrt(sinx)) is equal to

    Text Solution

    |

  2. If alpha and beta are roots of the equation ax^2+bx +c=0, then lim(xr...

    Text Solution

    |

  3. If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim(xto...

    Text Solution

    |

  4. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

    Text Solution

    |

  5. If F(x) = {(sin{cosx})/(x-pi/2),x!=pi/2 and 1,x=pi/2, where {.} repres...

    Text Solution

    |

  6. The value of lim(xrarr oo) 1+(1)/(x^n)^x,ngt 0, is

    Text Solution

    |

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

    Text Solution

    |

  8. lim(xrarr oo) (n^p sin^2(n!))/(n+1),0ltplt1, is equal to

    Text Solution

    |

  9. If lim(xrarr0) (cosx+a sinbx)^(1//x)= e^2, then the values of a and b ...

    Text Solution

    |

  10. lim(xrarr2)(sum(r=1)^(n)x^r-sum(r=1)^(n)2^r)/(x-2) is equal to

    Text Solution

    |

  11. If alpha is a repeated root of ax^2+bx +c=0 , then lim(xrarralpha)(sin...

    Text Solution

    |

  12. If f(x)={((tan^-1(x+[x]))/([x]-2x)[x]ne0,,),(0[x]=0,,):} where [x] den...

    Text Solution

    |

  13. If [.] denotes the greatest intger function, then lim(xrarr0) (tan([-2...

    Text Solution

    |

  14. ("lim")(xvecoo)[(x^4sin(1/x)+x)/((1+|x|^3)]=

    Text Solution

    |

  15. lim(n to oo) (1+x)(1+x^(2))(1+x^(4))……………(1+x^(2n)),|x|lt1 is

    Text Solution

    |

  16. If phi(x)=lim(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the f...

    Text Solution

    |

  17. The value of lim(x to pi//2){1^(sec^2x) +2^(sec^2x) +3^(sec^2x)+.......

    Text Solution

    |

  18. If l =lim(xrarr0) (tanx^(n))/((tanx)^m), where m,n in N, then

    Text Solution

    |

  19. If lim(x->oo)((1+a^3)+8e^(1/ x))/(1+(1-b^3)e^(1/ x))=2, then there exi...

    Text Solution

    |

  20. lim(xrarr-1)((x^4+x^2+x+1)/(x^2-x+1))^((1-cos(x+1))/((x+1)^2)) is equa...

    Text Solution

    |