Home
Class 12
MATHS
The value of lim(x->1)(2-x)^(tan((pix)/2...

The value of `lim_(x->1)(2-x)^(tan((pix)/2))` is

(a)`e^(-2/pi)`

(b) `e^(1/pi)`

(c) `e^(2/pi)`

(d) `e^(-1/pi)`

A

`a=1//4`

B

`b=3//4`

C

`L=-1//32`

D

`L=1//32`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto1)lim(2-x)^("tan"(pix)/(2))=underset(xto1)lim{1+(1-x)}^("tan"(pix)/(2))`
`=e^(underset(xto1)lim(1-x)"tan"(pix)/(2))`
`=e^(underset(xto1)lim(1-x)cot((pi)/(2)-(pix)/(2)))`
`=e^(underset(xto1)lim((1-x))/(tan((pi)/(2)-(pix)/(2))))`
`=e^((2)/(pi)underset(xto1)lim((pi)/(2)(1-x))/(tan((pi)/(2)(1-x))))`
`=e^(2//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

The value of lim_(x->0)(e^(x^2)-e^x+x)/(1-cos2x) is

Show that lim_(xrarr1)(1-x)tan((pix)/2)=2/pi

The value of ("lim")_(x->a)sqrt(a^2-x^2)cot(pi/2sqrt((a-x)/(a+x))) is (a) (2a)/pi (b) -(2a)/pi (c) (4a)/pi (d) -(4a)/pi

Evaluate: lim_(x->pi/2)(1+cos2x)/((pi-2x)^2)

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

The value of int_(-(pi)/(2))^((pi)/(2))(x^(2)cosx)/(1+e^(x))dx is

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

The value of lim x to pi/2( (2x-pi)/cosx) is

The value of lim_(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi)/(2n))]^(1/n) is

lim_(x->pi/4)(tan2(x-pi/4))/(x-pi/4)

CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

    Text Solution

    |

  2. The value of lim(ntooo) [(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^...

    Text Solution

    |

  3. ("lim")(xto1)(n x^(n+1)-(n+1)x^n+1)/((e^x-e)sinpix),\ where \n=100 , ...

    Text Solution

    |

  4. lim(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)=

    Text Solution

    |

  5. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

    Text Solution

    |

  6. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

    Text Solution

    |

  7. If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo then lim(xtoa){f(x)}^(g(x))=e^...

    Text Solution

    |

  8. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then

    Text Solution

    |

  9. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

    Text Solution

    |

  10. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e ...

    Text Solution

    |

  11. The value of lim(x->1)(2-x)^(tan((pix)/2)) is (a)e^(-2/pi) (b) e^...

    Text Solution

    |

  12. The value of ("lim")(xvecoo)(cos"x"/"m")^("m") is 1 (b) e (c) e^(-1...

    Text Solution

    |

  13. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

    Text Solution

    |

  14. lim(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ) is ...

    Text Solution

    |

  15. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is :

    Text Solution

    |

  16. The value of lim(xrarr0)(1^x+2^x+3^x+...+n^x)^(a//x)/n, is:

    Text Solution

    |

  17. The value of ("lim")(xvec1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal ...

    Text Solution

    |

  18. lim(xtooo) (x(logx)^(3))/(1+x+x^(2)) equals

    Text Solution

    |

  19. lim(x->oo)cot^(-1)(x^(-a)loga x)/(sec^(-1)(a^xlogx a)),(a >1)is equal ...

    Text Solution

    |

  20. The value of lim(ntooo)(e^(n))/((1+(1)/(n))^(n^(2)))is

    Text Solution

    |