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

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

Text Solution

Verified by Experts

Given `f(x)=sin(x^2)`
Let `g(x)=sinx `and `h(x)=x^2`
Now , `(goh)(x)`
`=g(h(x))`
...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.6|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.2|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise QUESTION|3 Videos

  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos

  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.4|5 Videos

Similar Questions

Explore conceptually related problems

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

Show that the function defined by f(x)=|cos x| is a continuous function.

Prove that the function defined by f(x)=tan x is a continuous function.

Prove that the function defined by f(x)=tan is a continuous function.

Is the function defined by f(x)={x+5, if x 1 a continuous function?

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

is f(x)=|x| a continuous function?

Show that f(x)=e^(5x) is a continuous function.

Show that the function f defined by f(x)=|1-x+|x|| is everywhere continuous.

Is the function defined by f(x)={{:(x, ifxle1),(5, ifx >1):} a continuous function at x=0,x=1 and x=2

NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Discuss the continuity of sine function.

    Text Solution

    |

  2. Prove that every rational function is continuous.

    Text Solution

    |

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

    Text Solution

    |

  4. Prove that the function defined by f(x) = t a n xis a continuous func...

    Text Solution

    |

  5. Examine whether the function f given by f(x)=x^2 is continuous at x =...

    Text Solution

    |

  6. Discuss the continuity of the function f given by f(x) = |x| at x = 0.

    Text Solution

    |

  7. Check the continuity of the function f given by f(x) = 2x + 3 at x = ...

    Text Solution

    |

  8. Prove that the identity function on real numbers given by f(x) = x is...

    Text Solution

    |

  9. Is the function defined by f(x) = |x|, a continuous function?

    Text Solution

    |

  10. Show that the function f given by f(x)={x^3+3ifx!=0 ;1ifx=0 is not ...

    Text Solution

    |

  11. Check the points where the constant function f(x) = kis continuous.

    Text Solution

    |

  12. Discuss the continuity of the function/given by f(x)=x^3+x^2-1.

    Text Solution

    |

  13. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

    Text Solution

    |

  14. If y= A sin x+ B cos x, then prove that (d^2y)/(dx^2)+y=0.

    Text Solution

    |

  15. Find (d^2y)/(dx^2), if y=x^3+tanx.

    Text Solution

    |

  16. Find (dy)/(dx), if x^(2/3)+y^(2/3)=a^(2/3).

    Text Solution

    |

  17. Find (dy)/(dx), if x=a(theta+sintheta), y=a(1-costheta).

    Text Solution

    |

  18. Find (dy)/(dx), if x=a t^2, y=2a t.

    Text Solution

    |

  19. Find (dy)/(dx), if x=acostheta,y=asintheta.

    Text Solution

    |

  20. Find (dy)/(dx), if y^x+x^y+x^x=a^b.

    Text Solution

    |