Home
Class 12
MATHS
For the function f(x)={((x^(3)-a^(3))/(...

For the function `f(x)={((x^(3)-a^(3))/(x-a)",",x ne a),(b" ,",x =a):}`, if f(x) is continuous at x = a, then b is equal to

A

`a^(2)`

B

`2a^(2)`

C

`3a^(2)`

D

`4a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Critical Thinking|80 Videos

  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={((sin pix)/(5x)",",x ne0),(k"," , x =0):} if f(x) is continuous at x = 0, then k is equal to

If f(x)={(log_((1-3x))(1+3x)",","for",x ne 0),(k",","for",x =0):} is continuous at x = 0, then k is equal to

Let f(x)=({:((3|x|+4tanx)/(x),",",x ne0),(k,",",x=0):} then f(x) is continuous at x = 0 for :

If f(x)=((3x+tan^(2) x)/x) is continuous at x=0 , then f(0) is equal to.

If the function f(x) defined by f(x)={(x"sin"(1)/(x)",", "for "x ne 0),(k",", "for " x=0):} is continuous at x = 0, then k is equal to

If f(x)={{:((log x-log3)/(x-3),"for "x ne 3),(c,"for "x =3):} is continuous at x = 3, then the value of c is

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

TARGET PUBLICATION-CONTINUITY-Competitive Thinking
  1. If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x ...

    Text Solution

    |

  2. For the function f(x)={((x^(3)-a^(3))/(x-a)",",x ne a),(b" ,",x ...

    Text Solution

    |

  3. The function 'f' is defined by f(x) = 2x - 1, if x gt 2, f(x) = k if ...

    Text Solution

    |

  4. f(x) = {(3x-8,",", "if"x le 5),(2k,",", "if"x gt 5):} is continuous at...

    Text Solution

    |

  5. If {:(f(x),=x^(2)+alpha,",","for"x ge 0),(,=2sqrt(x^(2)+1)+beta, ",","...

    Text Solution

    |

  6. In order that the function f(x) = (x+1)^(1/x) is continuous at x = 0, ...

    Text Solution

    |

  7. If f(x) = {((x^(2)+3x-10)/(x^(2)+2x-15),",", "when"x != -5),(a,",", "w...

    Text Solution

    |

  8. If f(x) = {((x^(2)-9)/(x-3),",", "if"x != 3),(2x+k,",", "otherwise"):}...

    Text Solution

    |

  9. If f(x) = {((sqrt(1+kx)-sqrt(1-kx))/(x), "if" -1 le x lt 0),((2x+k)/(x...

    Text Solution

    |

  10. If f(x) = {((sin 2x)/(5x), ",", "when" x != 0),(k, ",", "when" x = 0...

    Text Solution

    |

  11. If f(x) = {((3sin pix)/(5x), ",",x != 0),(2k, ",",x = 0):} is continu...

    Text Solution

    |

  12. If f(x) = |x-2|, then

    Text Solution

    |

  13. If f(x) = |x-b|, then the function

    Text Solution

    |

  14. If f(x) = {(1, ",", "when" 0 lt x le (3pi)/4),(2(sin) 2/9x, ",", "when...

    Text Solution

    |

  15. If f(x) = {((1-cosx)/x, ",", x != 0),(k, ",", x = 0):} is continuous a...

    Text Solution

    |

  16. If the function f(x) = {((cosx)^(1/x), ",", x != 1),(k, ",", x = 1):} ...

    Text Solution

    |

  17. If f(x) = {((log(e )x)/(x-1), ",", x != 1),(k, ",", x = 1):} is contin...

    Text Solution

    |

  18. The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined ...

    Text Solution

    |

  19. If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):...

    Text Solution

    |

  20. If f(x) = (e^(x^2)-cos x)/(x^(2)), "for" x != 0 is continuous at x = 0...

    Text Solution

    |