Home
Class 12
MATHS
Show that the function defined by f(x)=s...

Show that the function defined by `f(x)=sin (x^2)` is a continuous function.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    V PUBLICATION|Exercise QUESTION BANK|45 Videos

  • DETERMINANT

    V PUBLICATION|Exercise QUESTION BANK|136 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) defined by f(x)=sin(cosx) is a continuous function .

Prove that the function defined by f(x)= cosx^2 is a continuous function

Is the function defined by f(x)=x^2-sinx+5 continuous at x=pi?

Show that the function f:RrarrR given by f(x)=x+x^3 is a bijective function.

Is the function defined by f(x)={(x+3,ifxle1),(x-3,ifx>1):} a continuous function? Justify.

Show that the function f:RtoR defined by f(x)=2x-3 is one-one and onto. Find f^-1

Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):} is continuous or not .

Show that the function f(x)={(x^3+3ifxne0),(1ifx=0):} is not continuous at x=0

Find the derivative of the function given by f(x)=sin (x^2)

V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Prove that every rational function is continuous.

    Text Solution

    |

  2. Discuss the continuity of sine function.

    Text Solution

    |

  3. Show that the function defined by f(x)=sin (x^2) is a continuous funct...

    Text Solution

    |

  4. Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at...

    Text Solution

    |

  5. Examine the continuity of the function f(x)=2x^2-1 at x=3

    Text Solution

    |

  6. Examine the following functions for continuity f(x)=1/(x-5)

    Text Solution

    |

  7. Prove that the function f(x)=x^n is continuous at x=n, where n is a p...

    Text Solution

    |

  8. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

    Text Solution

    |

  9. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

    Text Solution

    |

  10. Find all points of discontinuity of f, where f is defined by f(x)={(|...

    Text Solution

    |

  11. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

    Text Solution

    |

  12. Find all points of discontinuity of f, where f is defined by f(x)={(x/...

    Text Solution

    |

  13. Examine the continuity of the function <be> f(x)={(x+1,xge1),(x^2+1,x<...

    Text Solution

    |

  14. Examine the continuity of the function f(x)={(x^3-3, if ,x le 2),...

    Text Solution

    |

  15. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

    Text Solution

    |

  16. Discuss the continuity of the function f(x)={(2 x , if , xlt0),( 0,...

    Text Solution

    |

  17. Find the derivative of the function given by f(x)=sin (x^2)

    Text Solution

    |

  18. Differentiate the function f(x)=sin [cos x^2] with respect to x.

    Text Solution

    |

  19. Differentiate the functions with respect to x: sin (x^2+5)

    Text Solution

    |

  20. Differentiate the functions with respect to x: cos (sin x)

    Text Solution

    |