Home
Class 12
MATHS
Let f(x)={(5^(1//x)"," , x lt 0),(lambda...

Let `f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):}` and `lambda in R`, then at x = 0

A

f is continuous whatever `lambda` may be

B

f is discontinuous

C

f is continuous only if `lambda = 0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    TARGET PUBLICATION|Exercise Competitive Thinking|63 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 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

If f(x)={(2x", for " x lt 0),(2x+1", for " x ge 0):} , then

{{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):}

Let f(x)={{:(2^([x]),, x lt0),(2^([-x]),,x ge0):} , then the area bounded by y=f(x) and y=0 is

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

If f(x) = {(x,",", x ge 0),(x^(2),",",x lt 0):} , then f(x) is

f(x)={{:(,[x]+[-x], x ne 0),(,lambda,x=0):} Find the value of lambda , f is continuous at x=0?

Let f(x)={{:(x^(2)-ax+1",", x lt 0),(b(1-x)^(3)",", x ge0):} . If is a differentiable function, then the ordered pair (a, b) is

If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):} , then

TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. If f(x)={((x)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):}, th...

    Text Solution

    |

  2. Which of the following functions is continuous at x = 0 ?

    Text Solution

    |

  3. Let f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):} and lambda in...

    Text Solution

    |

  4. If f(x) = (x-a)/(sqrt(x)-sqrt(a)), x != a, is continuous at x = a then...

    Text Solution

    |

  5. If f(x) = (sqrt(x+3)-2)/(x^(3)-1) , x != 1, is continuous at x = 1, th...

    Text Solution

    |

  6. If f(x)={((sqrt(1+kx)-sqrt(1-kx))/(x),",","for" -1 lex lt 0),(2x^(2)+3...

    Text Solution

    |

  7. If f(x) = {:((x^(4)-64x)/(sqrt(x^(2)+9)-5),",",x != 4),(k,",",x =4):} ...

    Text Solution

    |

  8. If f(x) = (tan(x^(2)-x))/(x), x != 0, is continuous at x = 0, then f(0...

    Text Solution

    |

  9. Function f(x) = (1-cos 4x)//(8x^(2)), " where " x != 0 , and f(x) = k...

    Text Solution

    |

  10. Let f(x) = {((1-cos 4x)/(x^(2))",",x lt 0),(a",",x = 0),((sqrt(x))/(sq...

    Text Solution

    |

  11. {:(f(x),=(1-cos 3x)/(x tan x),",","for" x != 0),(,=k, ",","for" x = 0)...

    Text Solution

    |

  12. For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...

    Text Solution

    |

  13. If {:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If f(x) ={((3sinx-sqrt(3)cosx)/(6x-pi),",",x != (pi)/6),(a, ",",x = pi...

    Text Solution

    |

  17. If f(x)=(1-sinx)/((pi-2x)^2),w h e nx!=pi/2a n df(pi/2)=lambda, the f(...

    Text Solution

    |

  18. If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0, then the value o...

    Text Solution

    |

  19. If the function f(x)=(2-sqrt(x+4))/(sin2x)(x ne 0) is continuous at x ...

    Text Solution

    |

  20. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

    Text Solution

    |