Home
Class 12
MATHS
lim(xrarr1)(sqrt1-cos2(x-1))/(x-1), is...

`lim_(xrarr1)(sqrt1-cos2(x-1))/(x-1)`, is

A

exists and it equals `sqrt(2)`

B

exists and it equals `-sqrt(2)`

C

does not exist because `(x-1)to0`

D

does not exist because left hand limit is not equal to right hand limit

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 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

lim_(xto1)(sqrt(1-cos2(x-1)))/(x-1) ,

lim_(xrarr0) (3sqrt(1+x-1))/(x)

lim_(xrarr0) (sqrt(1+x)-1)/(x)=?

lim_(xrarr2) (sqrt(3-x)-1)/(2-x)

lim_(xrarr1)(sqrt(1+x)-sqrt(1-x))/(1+x) is equal to

lim_(xrarr 1) (sqrt(4+x)-sqrt(5))/(x-1)

lim_(xrarr0)(cos 2x-1)/(cosx-1)

lim_( xrarr0) (1-cosx)/(x^(2))

The value of lim_(xrarr0) (sqrt(1-cosx^(2)))/(1-cos x) is

The value of lim_(xrarr 0) (1-cos(1-cos x))/(x^4) is equal to

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
  1. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

    Text Solution

    |

  2. value of lim(x->0)(1-cos^3x)/(xsinx*cosx) is

    Text Solution

    |

  3. lim(xrarr1)(sqrt1-cos2(x-1))/(x-1), is

    Text Solution

    |

  4. Evaluate the following limits (i) lim(x to (pi)/(2)) tan^(2) x [sqr...

    Text Solution

    |

  5. The value of lim(xrarr 0) (1-cos(1-cos x))/(x^4) is equal to

    Text Solution

    |

  6. The value of lim (xto0) (cos (sin x )- cos x)/(x ^(4)) is equal to :

    Text Solution

    |

  7. The value of underset(xto1)lim(2-x)^(tan((pix)/(2))) is

    Text Solution

    |

  8. The value of lim(xrarroo) ((3x-4)/(3x+2))^(((x+1)/3)) is

    Text Solution

    |

  9. lim(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

    Text Solution

    |

  10. The value of lim(xrarr0) ((1+tanx)/(1+sin x))^(cosec x) , is

    Text Solution

    |

  11. lim(x rarr 0)((5x^2+1)/(3x^2+1))^(1//x^2)

    Text Solution

    |

  12. Evaluate: ("lim")(n→oo)x[tan^(-1)((x+1)/(x+2))-tan^(-1)(x/(x+2))]

    Text Solution

    |

  13. The value of lim(x->0) ( int0 ^ (x^2) cost^2 dt)/( xsin x) is

    Text Solution

    |

  14. ("lim")(xvec0)(1n(1+2h)-21 n(1+h))/(h^2)=

    Text Solution

    |

  15. The value of lim(xrarr1)(log5 5x)^(logx5) , is

    Text Solution

    |

  16. The value of lim(xrarr1)(log2 2x)^(logx5), is

    Text Solution

    |

  17. lim(x->0) (sinx^n)/((sinx)^m),(mltn), is equal to (a) 1 (b) 0 (c) n...

    Text Solution

    |

  18. If 0lt xlty, then lim(xrarroo) (y^n+x^n)^(1//n) is equal to

    Text Solution

    |

  19. Evaluate the limit: ("lim")(xvecoo)[sqrt(a^2x^2+a x+1)-sqrt(a^2x^2+1)]

    Text Solution

    |

  20. lim(xrarr1)(1-x)tan((pix)/2) is equal to

    Text Solution

    |