Home
Class 12
MATHS
Let f(x)={(1/(x+[x]),if xlt0),(-1,if xge...

Let `f(x)={(1/(x+[x]),if xlt0),(-1,if xge0):}` Examine the continuity of f(x) at x=0.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x) at x=0.

Examine the continuity of f(x)= sin (pi(x))/2 at x = 0.

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 lambda ,is the function f(x)={(lambdax^2-2x,if xle0),(4x+1,ifx>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 ?

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

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

For what value of lamda is the function f(x)={{:(lamda(x^(2)-2x)", if "xle0),(4x+1", if "xgt0):} continuous at x=0 ? What about continuity at x=1 ?

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  2. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1

    Text Solution

    |

  3. Let f(x)={(1/(x+[x]),if xlt0),(-1,if xge0):} Examine the continuity of...

    Text Solution

    |

  4. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

    Text Solution

    |

  5. Find the equation of tangents and normals to the parabola y^2=4ax at t...

    Text Solution

    |

  6. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  7. Evaluate inte^x((1+sinx)/(1+cosx))dx.

    Text Solution

    |

  8. Evaluate the integral: int(x^2-4)/(x-2)dx

    Text Solution

    |

  9. Solve the following differential equations (x+tany)dy= sin 2y ""dx

    Text Solution

    |

  10. Evaluate int0^7 [x/3]dx

    Text Solution

    |

  11. Prove that the point (1,2,3),(-1,1,0),(2, 1, 3) and (1, 1, 2) are copl...

    Text Solution

    |

  12. If veca and vecb are unit vectors represented by the adjacent sides of...

    Text Solution

    |

  13. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

    Text Solution

    |

  14. Find the angle which a diagonal of a cube makes with one of its edges.

    Text Solution

    |

  15. Find the value of k for which A (1,0,3), B(-1,2,4), C(1,2,1) and D(k,2...

    Text Solution

    |

  16. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

    Text Solution

    |

  17. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

    Text Solution

    |

  18. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

    Text Solution

    |

  19. Find the equation of the tangent and normal to the curve y(x-2)(x-3)-x...

    Text Solution

    |

  20. Show that the semivertical angle of a cone of given slant height is ta...

    Text Solution

    |