Home
Class 12
MATHS
f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} ...

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

Promotional Banner

Topper's Solved these Questions

  • INTEGRATION AREA UNDER PLANE CURVES DIFFERENTIAL EQUATION

    USHA PUBLICATION|Exercise EXERCISE|89 Videos

Similar Questions

Explore conceptually related problems

Test differentiability and continuity of the following functions. f(x) = {(x sin (1/x), x ne 0), (0, x = 0) :} at x = 0.

Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x=0

Examine the continuity of the function f(x)={{:((|sinx|)/(x)", "x!=0),(1", "x=0):} at x=0

Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][x^2], xne0),(0, x=0):} is onto but not one-to-one.

Examine the continuity of the following functions at indicated points. f(x)={((1+2x)^(1/2)if xne0),(e^2 if x=0 at x=0):}

Examine continuity and differentiability f(x) = {[xsin1/x,if x!=0],[0,ifx=0]:} at x=0 .

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

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

A function f(x) is defined as follows : f(x)={(x^(2)"sin"(1)/(x)", if "x!=0),(0", if "x=0):} show that f(x) is differentiable at x=0.

USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. Find the derivative of the following functions from definition sin^2x.

    Text Solution

    |

  2. Find the derivative of the following functions from definition sqrt(ta...

    Text Solution

    |

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

    Text Solution

    |

  4. Test the differentiability of the following functions f(x)=x/(1+absx)a...

    Text Solution

    |

  5. If y = tan^-1((acosx-bsinx)/(bcosx+asinx)), then find (dy)/(dx)

    Text Solution

    |

  6. If y = tan^-1(secx+tanx), then find (dy)/(dx).

    Text Solution

    |

  7. Find (dy)/(dx), if y=sin^-1((sqrt(1+x)+sqrt(1-x))/2), -1ltxlt1

    Text Solution

    |

  8. Find (dy)/(dx), if x=sqrt(sin2u) and y=sqrt(cos2u)

    Text Solution

    |

  9. Find (dy)/(dx), if x=a(t-sint), y=a(1-cost)at t=(pi)/2

    Text Solution

    |

  10. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  11. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

    Text Solution

    |

  12. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

    Text Solution

    |

  13. Find the intervals where the following functions are (a) increasing an...

    Text Solution

    |

  14. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

    Text Solution

    |

  15. Find the points on the curve x^2+y^2-2x-4y+1=0,where the tangent is pa...

    Text Solution

    |

  16. Find the equations of the tangent and the normal to the curve y = (x-7...

    Text Solution

    |

  17. Find the angle of intersection of two curves y =2^x and y=5^x

    Text Solution

    |

  18. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

    Text Solution

    |

  19. Show that f(x)=(logx)/xhas minimum value at x=e

    Text Solution

    |

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

    Text Solution

    |