Home
Class 12
MATHS
Determine if f defined by f(x) = {(x^(2)...

Determine if f defined by `f(x) = {(x^(2)"sin" (1)/(x)",","if" x ne 0),(0",","if" x= 0):}` is a continuous function?

Text Solution

Verified by Experts

The correct Answer is:
x=0
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Long Answer Type Questions)|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Objective Type Questions)|28 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice Work|96 Videos

  • BOARD'S QUESTION PAPER MARCH - 2020

    KUMAR PRAKASHAN|Exercise PART - B (Section - C)|4 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Paper-4 (Section-D)|2 Videos

Similar Questions

Explore conceptually related problems

f(x) = {((|x|)/(x)",","if" x ne 0),(0",","if" x= 0):}

Prove that f(x)= {((sin x)/(x)+ cos x ",",x ne 0),(2",",x=0):} is a continuous function at x= 0

Is the function defined by f(x)= {(x+5",","if" x le 1),(x-5",","if" x gt 1):} a continuous function?

Prove that the function f defined by f(x) = {((x)/(|x|+ 2x^(2))",","if" x ne 0),(k,"if" x = 0):} remains discontinuous at x=0, regardless the choice of k

Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous function at x= 0.

For what value of lamda is the function defined by f(x)= {(lamda(x^(2)-2x)",","if" x le 0),(4x+1",","if" x gt 0):} continuous at x=0 ? What about continuity at x=1?

f(x)= {((|sin x|)/(x)",",x ne 0),(1",",x=0):} Examine the continuity of f(x), x= 0

Examine the continuity of the function f(x) = {(|x|.cos ((1)/(x))",","if" x ne 0),(0",","if" x = 0):} at x= 0

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Show that the function f(x)= |sinx + cos x| is continuous at x= pi

    Text Solution

    |

  2. Examine the differentiability of f, where f is defined by f(x) = {(x...

    Text Solution

    |

  3. Determine if f defined by f(x) = {(x^(2)"sin" (1)/(x)",","if" x ne 0),...

    Text Solution

    |

  4. Examine the continuity of the function f(x)= {(1+x",","if " x le 2),(5...

    Text Solution

    |

  5. Show that f(x) = |x-5| is continuous but not differentiable at x= 5

    Text Solution

    |

  6. A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for ...

    Text Solution

    |

  7. Differentiate 2^(cos^(2)x)

    Text Solution

    |

  8. Differentiate (8^(x))/(x^(8))

    Text Solution

    |

  9. Differentiate log (x + sqrt(x^(2) + a))

    Text Solution

    |

  10. Differentiate the following with respect to x: log [log (log x^(5))]

    Text Solution

    |

  11. Differentiate sin sqrtx + cos^(2) sqrtx

    Text Solution

    |

  12. Differentiate sin^(n) (a x^(2) + bx + c)

    Text Solution

    |

  13. Differentiate cos (tan sqrt(x+ 1))

    Text Solution

    |

  14. Differentiate sin x^(2) + sin^(2)x + sin^(2) (x^(2))

    Text Solution

    |

  15. Differentiate sin^(-1) ((1)/(sqrt(x + 1)))

    Text Solution

    |

  16. Differentiate (sin x)^(cos x)

    Text Solution

    |

  17. Differentiate sin^(m) x.cos^(n) x

    Text Solution

    |

  18. Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)

    Text Solution

    |

  19. Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (...

    Text Solution

    |

  20. Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt...

    Text Solution

    |