Home
Class 12
MATHS
What is the value of lim(xto0) (cos(ax)-...

What is the value of `lim_(xto0) (cos(ax)-cos(bx))/(x^(2))`

A

a-b

B

a+b

C

`(b^(2)-a^(2))/(2)`

D

`(b^(2)+a^(2))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Consider `underset(xto0)lim(cosax-cosbx)/(x^(2))`
`underset(xto0)lim(-asinax+bsinbx)/(2x)`
(using L' Hospital's rule)
`=(b^(2)-a^(2))/(2)(becausecos0=1)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

What is the value of lim_(xto0) (sinx)/(x) ?

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

The value of lim_(xto0)(x cosx-log(1+x))/(x^(2)) is

What is the value of lim_(xto0) (sin|x|)/(x) ?

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

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Consider the following statements: I. f(x)=|x-3| is continuous at x=...

    Text Solution

    |

  2. Consider the function f:Rto{0,1} such that f(x)={{:(1","if ,x" is ra...

    Text Solution

    |

  3. What is the value of lim(xto0) (cos(ax)-cos(bx))/(x^(2))

    Text Solution

    |

  4. If f(x)=2x+7andg(x)=x^(2)+7,x""inR, then what are values of x for whic...

    Text Solution

    |

  5. What is lim(xto0) (a^(x)-b^(x))/(x) equal to?

    Text Solution

    |

  6. If the function f(x)=(x(x-2))/(x^(2)-4),xnepm2 is continuous at x=...

    Text Solution

    |

  7. At how many points is the fucntion f(x)=[x] discontinuous?

    Text Solution

    |

  8. If f(x)=(2)/(3)x+(3)/(2),x""inR, then what is f^(-1)(x) equal to ?

    Text Solution

    |

  9. What is lim(xtooo) (sqrt(a^(2)x^(2)ax+1)sqrt(a^(2)x^(2)+1)) equal to?

    Text Solution

    |

  10. What is the value of k for which the following fucntion f(x) is contin...

    Text Solution

    |

  11. Which one of the following is correct in respect of the function f(x)=...

    Text Solution

    |

  12. Consider the following statements: I. f(x)=|x-3| is continuous at x=...

    Text Solution

    |

  13. What is lim(xto0) x^(2)sin((1)/(x)) equal to?

    Text Solution

    |

  14. What is lim(xto-2)((1+2)/(x^(3)+8))

    Text Solution

    |

  15. If f(x)f[xy]=f[x]f[y] then f[t] may be of the form:

    Text Solution

    |

  16. Which one of the following functions is differentiable for all real va...

    Text Solution

    |

  17. What is lim(xto0) (sqrt(1+x-1))/(x)

    Text Solution

    |

  18. What is lim(xto0) (2(1-cosx))/(x^(2) equal to?

    Text Solution

    |

  19. Consider the following : 1. lim(xto0) (1)/(x) exists. 2. lim(xto0)...

    Text Solution

    |

  20. Which one of the following is correct in respect of the function f(x)=...

    Text Solution

    |