Home
Class 11
MATHS
If f(x)=sqrt((x-sinx)/(x+cos^2x)), then ...

If `f(x)=sqrt((x-sinx)/(x+cos^2x))`, then `lim_(x rarr infty)f(x)` is

A

0

B

`infty`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If f(x)=1/3{f(x+1)+5/(f(x+2)}} and f(x) gt 0 for all x in R , then lim_(x rarr infty)f(x) is

Statement - I: if lim_(x to 0)((sinx)/(x)+f(x)) does not exist, then lim_(x to 0)f(x) does not exist. Statement - II: lim_( x to 0)(sinx)/(x)=1

f(x)=sqrt([sin2x]-[cos2x]) :[.]GIF, then range of f(x)

Let f(x) (1-cos4x)/(x^(2)),g(x)=(sqrtx)/((sqrt(16+sqrtx))-4)and q(x)=(e^(2x)-x^(x)+1)/(x^(2x+e^(x)+1)),(x in R). lim_(xrarr0)f(x)

If the function f(x) satisfies lim_(xrarr1)(f(x)-2)/(x^(2)-1)=pi , evaluate lim_(xrarr1)f(x) .

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x

if: f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(sqrt(1+cot^2x)), then find the range of f(x)

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

If f (x) = tan ^(-1) ((cos x- sinx)/(cos x+ sin x)) then the value of (d)/(dx) f(x) is-

If f(x)=2x+cos^(-1) x+log (sqrt(1+x^(2))-x) , then f(x) is-

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f is an even function such that lim(hrarr0)(f(h)-f(0))/h has some f...

    Text Solution

    |

  2. The values of constants a and b so as to make the function f(x)={(1/|x...

    Text Solution

    |

  3. If f(x)=sqrt((x-sinx)/(x+cos^2x)), then lim(x rarr infty)f(x) is

    Text Solution

    |

  4. Number of points at which f(x) = |x^2+x|+|x-1| is non-differentiable i...

    Text Solution

    |

  5. If lim(x rarr 0)(((a-n)nx-tanx)sinnx)/x^2=0, where n is non zero real ...

    Text Solution

    |

  6. lim(x rarrpi/4)(int2^(sec^2x) f(t)dt)/(x^2-pi^2/16)

    Text Solution

    |

  7. The value of lim(x rarr0)(int0^(x^2) cost^2dt)/(x sin x) is

    Text Solution

    |

  8. If f(x)=1/3{f(x+1)+5/(f(x+2)}} and f(x) gt 0 for all x in R, then lim(...

    Text Solution

    |

  9. If phi(x)=lim(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)), then

    Text Solution

    |

  10. Let f(x) = [x^3 - 3] where [.] denotes the greatest integer function T...

    Text Solution

    |

  11. If f(x)={(x[x], 0lexlt2),((x-1)[x], 2lexle3'):}, where [.] denotes the...

    Text Solution

    |

  12. If f(x)={(4, -3ltxlt-1),(5+x, -1lexlt0),(5-x, 0 lexlt2),(x^2+x-3, 2le...

    Text Solution

    |

  13. Let f(x)={((x-4)/(|x-4|)+a, xlt4),(a+b, x=4),((x-4)/(|x-4|)+b,x gt 4)...

    Text Solution

    |

  14. Let f(x)= {(a|x^2-x-2| /(2+x-x^2) , xlt2),(b, x = 2), ((x-[x])/(x-2), ...

    Text Solution

    |

  15. The value of f (0), so that function f(x) = (sqrt(a^2-ax+x^2)-sqrt(a^...

    Text Solution

    |

  16. Let f(x) = |x|-1|, then points where f(x), is not differentiable is/ar...

    Text Solution

    |

  17. Let f be twice differentiable function satisfying f(1) = 1, f(2) = 4, ...

    Text Solution

    |

  18. f(x)= min{1, cosx, 1-sinx}, -pilexlepi then

    Text Solution

    |

  19. Let f : R rarr R be any function. Define g : R rarr R by g(x)=|f(x)| f...

    Text Solution

    |

  20. If f(x) = lim(nrarr infty)(sinx)^(2n) where n in l^+ then f(x) is

    Text Solution

    |