Home
Class 12
MATHS
If f.g is continuous at x = 0 , then f ...

If `f.g` is continuous at `x = 0` , then f and g are separately continuous at `x = 0`.

Text Solution

Verified by Experts

Let `f(x) = sinx` and `g(x) = cotx`
`:. f(x). g(x) = sinx. (cosx)/(sinx) = cosx`
which is continuous at `x = 0` but `cot x` is not continuous at `x = 0`.
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

If f(x) is continuous at x=0, then f(0) is defined as where

Let f and g be two real functions; continuous at x=a Then f+g and f-g is continuous at x=a

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

If f and g are both continuous at x = a, then f-g is

Let f and g be two real functions;such that fog is defined.If g is continuous at x=a and f is continuous at g(a); show that fog is continuous at x=a

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

A function f(x) is defined as follows f(x)={(sin x)/(x),x!=0 and 2,x=0 is,f(x) continuous at x=0? If not,redefine it so that it become continuous at x=0 .

Let f and g be two real functions; continuous at x=a Then fg and (f)/(g) ia continous at x=a; provided g(a)!=0

NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. The function f(x) = e^(|x|) is

    Text Solution

    |

  2. If f(x) = x^(2)sin'(1)/(x), where x ne 0, then the value of the functi...

    Text Solution

    |

  3. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

    Text Solution

    |

  4. If f(x) = |sinx|, then

    Text Solution

    |

  5. If y = log ((1-x^(2))/(1+x^(2))), then (dy)/(dx) is equal to

    Text Solution

    |

  6. If y = sqrt(sinx+y), then (dy)/(dx) is equal to

    Text Solution

    |

  7. The derivative of cos^(-1)(2x^(2)-1) w.r.t. cos^(-1) is

    Text Solution

    |

  8. If x = t^(2) and y = t^(3), then (d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  9. The value of c in Rolle's theorem for the function f(x) = x^(3) - 3...

    Text Solution

    |

  10. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  11. An example of a function which is continuous every where but fails to...

    Text Solution

    |

  12. Derivative of x^(2) w.r.t. x^(3) is "……."

    Text Solution

    |

  13. If f(x) = |cosx|, then f'(pi/4) is equal to "……."

    Text Solution

    |

  14. For the curve sqrt(x) + sqrt(y) = 1, (dy)/(dx) at (1/4,1/4) is "……….".

    Text Solution

    |

  15. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

    Text Solution

    |

  16. If f is continuous on its domain D; then |f| is also continuous on D

    Text Solution

    |

  17. If f is continuous on its domain D; then |f| is also continuous on D

    Text Solution

    |

  18. The composition of two continuous function is a continuous function.

    Text Solution

    |

  19. Trigonometric and inverse trigonometric functions are differentiable ...

    Text Solution

    |

  20. If f.g is continuous at x = 0 , then f and g are separately continuou...

    Text Solution

    |