Home
Class 12
MATHS
If f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+...

If `f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x))` is continuous at `x=0` then `f(0)`

A

`-a sqrt(a)`

B

`a sqrt(a)`

C

`-sqrt(a)`

D

`sqrt(a)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    NIKITA PUBLICATION|Exercise MCQS|77 Videos

  • DEFINITE INTEGRAL

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|243 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(sqrt(a^(2)-ax+x^(2))-sqrt(a^(2)+ax+x^(2)))/(sqrt(a+x)-sqrt(a-x)) is continuous at x=0 then f(0)

The value of f(0), so that the function f(x)=(sqrt(a^(2)-ax+x^(2))-sqrt(a^(2)+ax+x^(2)))/(sqrt(a+x)-sqrt(a-x)) becomes continuous for all x, given by a^((3)/(2))( b) a^((1)/(2))(c)-a^((1)/(2))(d)-a^((3)/(2))

The value of f(0) , so that the function f(x) = (sqrt(a^(2)-ax+x^(3))-sqrt(a^(2)+ax+x^(2)))/(sqrt(a+x)-sqrt(a-x)) become continuous for all x, is given by

Value of f(0) so that f(x)=(sqrt(2+x)-sqrt(2))/(x) is continuous at x=0 is

If f(x) = (sqrt(4 +x)-2)/(x) is continuous x=0 then the value of f(0) is

f(x)=sqrt(x-4-2sqrt(x-5))

Prove that f(x)=sqrt(|x|-x) is continuous for all x>=0

Prove that f(x)=sqrt(|x|-x) is continuous for all x>=0

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x) is continuous at x=0, where f(x)=(sqrt(1+x)-root3(1+x))/(x), f...

    Text Solution

    |

  2. If f(x) is continuous at x=4, where f(x)=(x^(4)-64x)/(sqrt(x^(2)+9)-5)...

    Text Solution

    |

  3. If f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x)) is...

    Text Solution

    |

  4. If f(x) is continuous at x=2a, where f(x)=(sqrt(x)-sqrt(2a)+sqrt(x-2a)...

    Text Solution

    |

  5. If f(x) is continuous at x=sqrt(2), where f(x)=(sqrt(3+2x)-(sqrt(2)+1)...

    Text Solution

    |

  6. If f(x) is continuous at x=5, where f(x)=(sqrt(3+sqrt(4+x))-sqrt(6))/(...

    Text Solution

    |

  7. If f(x) is continuous at x=0, where f(x)=sin x-cos x, for x!=0, then ...

    Text Solution

    |

  8. If f(x) is continuous at x=pi/2, where f(x)=(sqrt(2)-sqrt(1+sin x))/(...

    Text Solution

    |

  9. If f(x) is continuous at x=pi/4, where f(x)=(1-tanx)/(1-sqrt(2)sin x),...

    Text Solution

    |

  10. If f(x) is continuous at x=0, where f(x)=(sin (pi cos^(2)x))/(x^(2)), ...

    Text Solution

    |

  11. If f(x) is continuous at x=(pi)/(4) where f(x)=(2sqrt(2)-(cos x+sin x)...

    Text Solution

    |

  12. If f(x) is continuous at theta= pi/4, where f(theta)={:{((1-tan theta...

    Text Solution

    |

  13. The function f(x)=(1-sinx+cosx)/(1+sinx+cosx) is not defined at x=pi....

    Text Solution

    |

  14. If f(x) is continuous at x=pi/2, where f(x)=(cos x )/(sqrt(1-sinx)), ...

    Text Solution

    |

  15. If f(x) is continuous at x= pi/4, where f(x)=(cos x- sin x)/(cos 2x),...

    Text Solution

    |

  16. If f(x) is continuous at x= pi/4, where f(x)=(2-cosec^(2)x)/(cot x-1)...

    Text Solution

    |

  17. If f(x) is continuous at x=0, where f(x)=(sin(x^(2)-x))/(x), for x!=0...

    Text Solution

    |

  18. If f(x) is continuous at x=0, where f(x) = {:{((x cos x+3tan x)/(x^(2...

    Text Solution

    |

  19. If f(x) is continuous at x=0, where f(x)=(sin (a+x)-sin (a-x))/(tan (a...

    Text Solution

    |

  20. f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f ...

    Text Solution

    |