Home
Class 12
MATHS
lim(x->1)(1-x^2)/(sin2pix) is equal to ...

`lim_(x->1)(1-x^2)/(sin2pix)` is equal to

(a)`1/(2pi)`

(b) `-1/pi`

(c) `(-2)/pi`

(d) none of these

A

0

B

`oo`

C

-2

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto1)lim(1-x^(2))/(sin2pix)=-underset(xto1)lim(2pi(1-x)(1+x))/(2pisin(2pi-2pix))`
`=underset(xto1)lim((2pi-2pix))/((2pi-2pix))(1+x)/(2pi)=(-1)/(pi)`
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

lim_(xtooo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logx dx is equal to (a) -pi/2logpi (b) 0 (c) pi/2log2 (d) none of these

cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is equal to (a) sqrt(2)-1 (b) pi/4 (c) (3pi)/4 (d) none of these

("lim")_(xto0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equals to (a)1 (b) 0 (c) 2 (d) none of these

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these

lim_(x->(pi/2)) (1-sinx)tanx =

int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e+1 (b) 1-e (c) e-1 (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to (a) 0 (b) 2pi (c) pi (d) none of these

lim_(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 (c) pi (d) 2pi

CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

    Text Solution

    |

  14. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

    Text Solution

    |

  15. The value of lim(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is (a)4 (b) ...

    Text Solution

    |

  16. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

    Text Solution

    |

  17. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

    Text Solution

    |

  18. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

    Text Solution

    |

  19. If f(x)=lim(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal...

    Text Solution

    |

  20. lim(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x ...

    Text Solution

    |