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

Show that the function f(x) given by
`f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):}` is continuous at x =0

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 3

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS |13 Videos

  • SAMPLE PAPER 3

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS |13 Videos

  • SAMPLE PAPER 2

    ARIHANT PUBLICATION|Exercise Long Answer Type Questions|13 Videos

  • SAMPLE PAPER 4

    ARIHANT PUBLICATION|Exercise Long Answer Type Questions|13 Videos

Similar Questions

Explore conceptually related problems

Find the value of a, so that the function f(x) is defined by f(x)={{:((sin^(2)"ax")/(x^(2))", "x!=0),("1, "x=0):} may be continuous at x=0.

Show that the function f(x)={{:((sinx)/(x)+cosx", if "x!=0),(2", if "x=0):} is continuous at x=0 .

Find the value of a such that the function f defined by f(x)={{:((sinax)/(sinx), "if", x ne 0),((1)/(a), "if", x=0):} is continuous at x=0

If the function f(x) defined by f(x)={((log(1+ax)-log(1-bx))/(k)", if "x!=0),(" k, if "x=0):} is continuous at x=0 , then find the value of k.

Find the value of a such that the function f defined by f(x)={((sinax)/(sinx) if xne0),(1/a if x=0):} is continuous at x=0.

For what value of k, the function f(x)={((tan2x)/(x)", if "x!=0),(k", if "x=0):} is continuous at x=0 ?

For what value of k, the function f(x)={{:((sin2x)/(x)", "x!=0),(k", "x=0):} is continuous at x=0 ?

f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

ARIHANT PUBLICATION-SAMPLE PAPER 3 -SHORT ANSWER TYPE QUESTIONS
  1. If A = [{:(0,2),(3,-4):}] and KA = [{:(0, 3a),(2b, 24):}], then find v...

    Text Solution

    |

  2. Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (...

    Text Solution

    |

  3. Find the inverse of the following matrix [{:(1,3,-2),(-3,0,-1),(2,1,...

    Text Solution

    |

  4. A card from a pack of 52 playing cards is lost. From the remaining car...

    Text Solution

    |

  5. How many times must a man toss a fair coin so that the probability of ...

    Text Solution

    |

  6. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

    Text Solution

    |

  7. Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if ...

    Text Solution

    |

  8. Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...

    Text Solution

    |

  9. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

    Text Solution

    |

  10. If x = 3 sin t - sin 3t, y = 3 cos t - cos 3t, find (dy)/(dx) at t = (...

    Text Solution

    |

  11. Evaluate int(2x^(3) + 3x^(2) +5x+2) dx

    Text Solution

    |

  12. Solve the following differerntial equation x (dy)/(dx) + y = x cos x +...

    Text Solution

    |

  13. Evaluate int (x ^(2) +1)/( (x +1) ^(2)) dx

    Text Solution

    |

  14. Evaluateint (cosxtan x )/((sec x + tan x )) dx

    Text Solution

    |

  15. Find the area of region included between the parabola 4y = 3x^(2) and ...

    Text Solution

    |

  16. Find the direction consines of the perpendicular from the origin to th...

    Text Solution

    |

  17. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

    Text Solution

    |

  18. Using vectors, find the area of the Delta ABC, whose vertices are A(1,...

    Text Solution

    |

  19. Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y ...

    Text Solution

    |

  20. If a xx b = c xx d and a xx c = b xxd , show that (a-d) is parallel to...

    Text Solution

    |