Home
Class 12
MATHS
Let f(x)={(absx/x,if xne0),(0,if x=0):} ...

Let `f(x)={(absx/x,if xne0),(0,if x=0):}` 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)={(1/(x+[x]),if xlt0),(-1,if xge0):} Examine the continuity of f(x) at x=0.

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

Examine the continuity of function f(x)=5x-3 at x=-3

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.

f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} 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)={{:((sinx)/(x)+cosx", if "x!=0),(2", 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

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

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

    Text Solution

    |

  2. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

    Text Solution

    |

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

    Text Solution

    |

  4. int(1+x^2)/(xsqrt(x^4+1))dx

    Text Solution

    |

  5. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

    Text Solution

    |

  6. int0^pi(xsinxdx)/(1+cos^2x)

    Text Solution

    |

  7. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

    Text Solution

    |

  8. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

    Text Solution

    |

  9. Prove that the sum of the vectors directed from the vertices to the mi...

    Text Solution

    |

  10. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

    Text Solution

    |

  11. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

    Text Solution

    |

  12. Prove the following by vector method. The diagonals of a rhombus are a...

    Text Solution

    |

  13. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

    Text Solution

    |

  14. int0^pi((xtanx)/(secx+tanx))dx

    Text Solution

    |

  15. Solve: (1+x^2)dy/dx+2xy-x^3=0

    Text Solution

    |

  16. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

    Text Solution

    |

  17. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

    Text Solution

    |

  18. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |

  19. If A=[(0,1,0),(-1,0,2),(0,0,1)], then show that A^3-A^2+I3=[(2,-1,0),(...

    Text Solution

    |

  20. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

    Text Solution

    |