Home
Class 12
MATHS
If f(x) = {:(a^(2)sin^(2)x+e^(2) cos^(2...

If `f(x) = {:(a^(2)sin^(2)x+e^(2) cos^(2)x", if " x le 0 ),(=e^(ax+b)", if " x gt 0):}` is continuous at x = 0 , then b = `…..`

A

2

B

` log |a|`

C

2 log |a|

D

1

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|11 Videos

  • DIFFERENTIAL EQUATIONS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|14 Videos

Similar Questions

Explore conceptually related problems

If f(x) {:(=(sin4x)/(5x)+a", if " x gt 0 ),( = 6x+4 -b ", if " x le 0):} is continuous at x = 0 , then : a+ b =

If f(x) {:( =(sin 4x)/(5x)+a", if " x gt 0 ),(=x + 4 - b ", if " x le 0 ) :} is continuous at x= 0 , then a+ b - = ……

Given f(x) {:(=x^(2)+a", if "x le 0 ),(= 2 sqrt(1+x^(2))+b ", if " x gt 0 ) :} and f(-1)=2 . If f is continuous at x = 0 , then (a,b) -= …..

If f(x) {:(=x+a", if " x lt 0 ),(= x ", if " 0 le x le 1 ),(=b-x ", if " x gt 1 ) :} is continuous in [-2,2] , then a+b is

If f(x) {: (=(8^(x) - 4^(x)-2^(x)+1)/(x^(2)) ", ... " x gt 0), ( = e^(x) sin x + pix + lambda . "In 4, ... " x le 0):} is continuous at x = 0 , then : lambda =

If f(x) {:(=x^(2)+ax+b", if "0 le x lt 2 ),(= 3x+2", if " 2 le x le 4 ),(=2ax + 5b ", if " 4 lt x le 8 ) :} is continuous on [ 0,8] then a-b = ……

If f(x) = {(sin x, ",", "if" x le 0),(x^(2)+a^(2), ",", "if" 0 lt x lt 1),(bx + 2, ",", "if" 1 le x le 2),(0, ",", "if" x gt 2):} is continuous on R, then a + b + ab =

If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, then

If f(x) ={(a^2 cos^2 x+b^2 sin^2 x"," , x 0):} f(x) is continuous at x=0 then

If f(x) = ((e^(mx)-1)sin mx)/(4x^(2)), x !=0 and f(0) = 9 ,is continuous at x = 0 , then m = ….

MARVEL PUBLICATION-CONTINUITY F FUNCTIONS-MULTIPLE CHOICE QUESTIONS
  1. If f(x) = {:((8^(x)-2^(x))/(k^(x)-1)", if " x != 0 ),(=2", ...

    Text Solution

    |

  2. If f(x) (10^(x)+7^(x)-14^(x)-5^(x))/(1-cos x), x != 0 is continuous ...

    Text Solution

    |

  3. If f(x) = {:(a^(2)sin^(2)x+e^(2) cos^(2)x", if " x le 0 ),(=e^(ax+b...

    Text Solution

    |

  4. Value of a so that f(x) = (sin^(2)ax)/(x^(2)), x != 0 and f(0) = 1 ...

    Text Solution

    |

  5. Value of f(0) so that f(x) = (sin(x^(2)+4x)-sin 4x)/(x tan x ) x !...

    Text Solution

    |

  6. At x = 0 , f(x) {:(=x-2", if " x lt 0 ),(= 1//2", if " x = 0...

    Text Solution

    |

  7. If f(x) {:(=-x^(2)", if " x le 0 ), (= 5x - 4 ", ...

    Text Solution

    |

  8. Function f(x)={{:(2x-1", if "x le 1 ),(x^(2)", if "1 ...

    Text Solution

    |

  9. If f(x) {:(=x^(2)-1", if "x lt 3 ),(= 2ax ", if "x le 3 )...

    Text Solution

    |

  10. If f(x) {: (=x^(3)", if " x lt 1//2 ),(= ax^(2)", if " x ge 1...

    Text Solution

    |

  11. If f(x) {:(=x+1", if " x le 1 ),(= 3 + ax^(2)", if "x gt 1 ...

    Text Solution

    |

  12. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

    Text Solution

    |

  13. If f(x) {:(=3k", if "x le 1/2 ),(= 3/2-2x " , if...

    Text Solution

    |

  14. If f(x) {:(=3x-4", if " 0 le x le 2 ),(= 2x + k ", if "2lt x ...

    Text Solution

    |

  15. Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"fo...

    Text Solution

    |

  16. Given f(x) {:(=x^(2)+a", if "x le 0 ),(= 2 sqrt(...

    Text Solution

    |

  17. If f(x) {:( =(sin 4x)/(5x)+a", if " x gt 0 ),(=x + 4 - b ", ...

    Text Solution

    |

  18. If f(x) {:(=x+a", if " x lt 0 ),(= x ", if " 0 le x ...

    Text Solution

    |

  19. If f(x) {:(=x^(2)+ax+b", if "0 le x lt 2 ),(= 3x+2", i...

    Text Solution

    |

  20. If f(x) {:(=x^(2)/a", if " 0 le x lt 1 ),(= a", ...

    Text Solution

    |