Home
Class 12
MATHS
Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-...

`Let f(x)=lim_(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)`. Then the set of values of x for which `f(x)=0` is

A

199

B

198

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given `g(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5)=0`
or`underset(ntooo)lim[((3)/(pi)tan^(-1)2x)^(2)]^(n)rarroo`
or`((3)/(pi)tan^(-1)2x)^(2)gt1`
or `|tan^(-1)2x|gt(pi)/(3)`
i.e., i.e.,`tan^(-1)2xlt-(pi)/(3)" or "tan^(-1)2xgt(pi)/(3)`
`2xlt1sqrt(3)" or "2xgtsqrt(3),i.e.,|2x|gtsqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|20 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Matrix Match Type|5 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.8|8 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(x) is

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then f has

Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these

Let lim_(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a) . Then the value of f(4) is_________.

Let for all xgt0,f(x)=lim_(nto oo)n(x^((1)/(n))-1) , then

Let f(x) be a polynomial satisfying lim_(xtooo) (x^(2)f(x))/(2x^(5)+3)=6" and "f(1)=3,f(3)=7" and "f(5)=11. Then The value of f(0) is

Let f (x+(1)/(x))= x^(2) +(1)/(x^(2)) , x ne 0, then the value of f (x) is-

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

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

    Text Solution

    |

  2. lim(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x ...

    Text Solution

    |

  3. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

    Text Solution

    |

  4. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

    Text Solution

    |

  5. The value of lim(n->oo)[(2n)/(2n^2-1)cos((n+1)/(2n-1))-n/(1-2n)dot(n(-...

    Text Solution

    |

  6. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

    Text Solution

    |

  7. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

    Text Solution

    |

  8. ("lim")(xvecoo)(x^2tan1/x)/(sqrt(8x^2+7x+1))i se q u a lto: -1/(2sqrt...

    Text Solution

    |

  9. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

    Text Solution

    |

  10. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

    Text Solution

    |

  11. lim(x->1)(1-x^2)/(sin2pix) is equal to (a)1/(2pi) (b) -1/pi (...

    Text Solution

    |

  12. ("lim")(xto0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equals to (a)1 (b) 0 ...

    Text Solution

    |

  13. lim(y->0)((x+y)sec(x+y)-xsecx)/y is equal to (a) secx(xtanx+1) (b) x...

    Text Solution

    |

  14. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

    Text Solution

    |

  15. ("lim")(ntooo)sum(x=1)^(20)cos^(2n)(x-10) is equal to

    Text Solution

    |

  16. lim(xto-1)((x^4+x^2+x+1)/(x^2-x+1))^((1-cos(x+1))/((x+1)^(2)) is equal...

    Text Solution

    |

  17. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

    Text Solution

    |

  18. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

    Text Solution

    |

  19. The value of ("lim")(x->a)sqrt(a^2-x^2)cot(pi/2sqrt((a-x)/(a+x))) is (...

    Text Solution

    |

  20. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

    Text Solution

    |