Home
Class 12
MATHS
The value of lim(xto0) (1-(cosx)sqrt(cos...

The value of `lim_(xto0) (1-(cosx)sqrt(cos2x))/(x^(2))` is

A

`(1)/(3)`

B

`(1)/(2)`

C

`(1)/(6)`

D

`(5)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto0)lim(1-cosxsqrt(cos2x))/(x^(2))`
`underset(xto0)lim(1-cosxsqrt(cos2x")")(1+cosxsqrt(cos2x)))/(x^(2)"("1+cosxsqrt(cos2x")"))`
`=underset(xto0)lim(1-cos^(2)x(cos2x))/(2x^(2))`
`=underset(xto0)lim(1-cos^(2)x(2cos^(2)-1))/(2x^(2))`
`=underset(xto0)lim((1-cos^(2)x)(1+2cos^(2)x))/(2x^(2))`
`=underset(xto0)lim(sin^(2)x.(1+2cos^(2)x))/(2x^(2))`
`=(3)/(2)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise (Multiple)|18 Videos

  • LIMITS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.8|8 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

lim_(xto0)(1-cosx)/x^(2)

lim_(xto0)(1-cos(1-cosx))/(x^(4)) is

lim_(xto0)(1-cos^(2)x)/(xsin2x)

lim_(xto0)(sqrt2-sqrt(1+cosx))/(sin^(2)x)

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

lim_(xto0)(1-cos2x)/(2x^(2)) is

Evaluate lim_(xto0) (cosx)^(cotx).

Evaluate lim_(xto0) (sqrt(2)-sqrt(1+cosx))/(sin^(2)x).

The value of lim_(xto0) (2^(3x)-3^(2x))/x is

CENGAGE-LIMITS-Exercise (Single)
  1. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

    Text Solution

    |

  2. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The value of ("lim")(xvec1^-)(1-sqrt(x))/((ccos^(-1)x)^2) is 4 (b) ...

    Text Solution

    |

  6. ("lim")(xvecpi/2)(sin(xcosx)/("cos"(xsinx)i se q u a lto 0 (b) p/2 (...

    Text Solution

    |

  7. ("lim")(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the ...

    Text Solution

    |

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

    Text Solution

    |

  9. If f(x)=lim(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to ...

    Text Solution

    |

  10. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

    Text Solution

    |

  11. The value of ("lim")(xvecoo)((2^x^n)^1//e^x-(3^x^n)^1//e^x)/(x^n) (whe...

    Text Solution

    |

  12. ("lim")(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c)...

    Text Solution

    |

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

    Text Solution

    |

  14. ("lim")(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2(1/(m2...

    Text Solution

    |

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

    Text Solution

    |

  16. The value of lim(ntooo) [1/n+2] is

    Text Solution

    |

  17. ("lim")(xvec0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= -1 (b) 1 ...

    Text Solution

    |

  18. The value of lim(xto0) (2^(3x)-3^(2x))/x is

    Text Solution

    |

  19. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

    Text Solution

    |

  20. The value of lim(ntooo) [(1+2+3+...+n)/n^2] is

    Text Solution

    |