Home
Class 12
MATHS
How should we define f(x) = (log(1+ax)-l...

How should we define `f(x) = (log(1+ax)-log(1-bx))/x` at x = 0 so as to make it continuous, at x = 0

A

a-b

B

log a +log b

C

a+b

D

loga a/b

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos
  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log ((1+x)/(1-x)) , then

The value of f(x) at x = 0, so that the function f(x) = (2^(x)-2^(-x))/x, x ne 0 is continuous at x = 0

The function f(x) = (log (1+ax) - log(1-bx))/(x) is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0 is :

The value of f(0) for which the function : (log_(e) (1-ax) - log_(3) (1-bx))/(x) is continuous at x = 0 is :

Let f(x)=(x)/(1+x)-log(1+x) , when x gt 0 , then f is :

If f(x) = log_(a) (log_(a)x) , then f^(')(x) is

If f(x)= log_(x^(2))(log x) , then f(x) at x=e is

The function f(x) = ([log (1 + ax) - log (1-bx)])/(x) is not defined at x = 0. The value, which should be assrgned to f at x = 0. The value, which should be assrgned to f at x = 0 so that it is continuous at x = 0 is :

The function f(x)=(log(1+ax)-log(1-bx))/x is not defined at x=0 . The value which should be assigned to f at x=0 so that it is continuous at x=0 is

Find the relationship between a and b so that the function defined by f(x) = {(ax+1,if, x le 3),(bx+3,if, x gt 3):} is continuous at x = 3.

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If the function f(x) = {{:((x^(2)-(a+2)x + a)/(x-2),,x ne 2),(2,,x = 2...

    Text Solution

    |

  2. The value of f(0) so that the function f(x) = (2x-sin^(-1)x)/(2x+tan^(...

    Text Solution

    |

  3. How should we define f(x) = (log(1+ax)-log(1-bx))/x at x = 0 so as to...

    Text Solution

    |

  4. Which of the following is false ?

    Text Solution

    |

  5. If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 th...

    Text Solution

    |

  6. Let f(x) = {((sin pix)/(5x), x ne 0),(k, x =0):} If f(x) is continuous...

    Text Solution

    |

  7. The function f(x)=|x|+(|x|)/(x) is

    Text Solution

    |

  8. If f(x)={((1-cosx)/(x),xne0),(k, x=0):} is continuous at x=0 then k=

    Text Solution

    |

  9. If f(x) = {((sin 5x)/(x^(2)+2x), x ne 0),(k+1/2, x =0):} is continuous...

    Text Solution

    |

  10. Which one of the following is not true always?

    Text Solution

    |

  11. The points of discontinuity of f(x) = tan((pix)/(x+1))

    Text Solution

    |

  12. Let f(x) = {(-2sinx, x le -pi/2),(asinx +b, -pi/2 lt x lt pi/2),(cosx,...

    Text Solution

    |

  13. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

    Text Solution

    |

  14. Consider f(x)={{:((x^(2))/(|x|)","x!=0),(0","x=0.):}

    Text Solution

    |

  15. If the function f(x) = {((sin 3x)/x, x ne 0),(k/2, x = 0):} is continu...

    Text Solution

    |

  16. If f(x) = (x^(2)-10x +25)/(x^(2)-7x+10 for x ne 5 and f is continuous ...

    Text Solution

    |

  17. If f : R rarr R is defined by f(x) ={(a^(2)cos^(2)+b^(2)sin^(2)x, x le...

    Text Solution

    |

  18. If f(x) ={((sqrt(1+kx)- sqrt(1-kx))/x, -1 le x le0),(2x^(2)+3x-2, 0 le...

    Text Solution

    |

  19. If f(x) = {((1-sqrt2sinx)/(pi-4x), x ne pi/4),(a, x = pi/4):} is conti...

    Text Solution

    |

  20. The value of b for which the function : f(x) = {{:(5x-4,"if",0lt x le ...

    Text Solution

    |