Home
Class 12
MATHS
Show that f(x)={{:((cosax-cosbx)/(x^(2))...

Show that `f(x)={{:((cosax-cosbx)/(x^(2))," if " xne0),((1)/(2)(b^(2)-a^(2))," if "x=0):}"is continuous at 0"`

Text Solution

Verified by Experts

The correct Answer is:
x=0
Promotional Banner

Topper's Solved these Questions

  • SOLVED MODEL PAPER -7

    SRISIRI PUBLICATION|Exercise SECTION-C|7 Videos
  • SOLVED MODEL PAPER-2

    SRISIRI PUBLICATION|Exercise SOLVED MODEL PAPER-2(MATHS-1B)|24 Videos

Similar Questions

Explore conceptually related problems

Show that f(x)={{:((cos ax-cosbx)/(x^(2)),if x ne 0),(1/2 (b^(2)-a^(2)),if x =0):} where a and b are real constants is continuous at x = 0.

Is f defined by f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}" continuous"0 ?

Show that Lt_(xto0)(cosax-cosbx)/x^(2)=(b^(2)-a^(2))/2

Show that Lt_(xto0)(1-cosax)/(xsin2x)=a^(2)/4

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Evaluate {:("Lt"),(xrarr0):}(cosax-cosbx)/(x^(2))

Is f defined by f(x) = {((sin 2x)/x, if x != 0),(1, if x = 0):} continuous at 0?

f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =

f(x) = {{:((36^(x) - 9^(x) - 4^(x) + 1)/(2sin^(2) ((x)/(4)) )" if " x ne 0),(k " if " x = 0):} is continuous at x = 0 then k =

SRISIRI PUBLICATION-SOLVED MODEL PAPER-1-SOLVED MODEL PAPER-1(MATHS-1B)
  1. Find the angle between the planes 2x-y+z=6 and x+y+2z=7

    Text Solution

    |

  2. Show that Lt(x to0+)((2|x|)/x+x+1)=3.

    Text Solution

    |

  3. Evaluate Lt(x to0)((e^(3+x)-e^3)/x)

    Text Solution

    |

  4. If f(x) = a^x.e^(x^2) then find f'(x)

    Text Solution

    |

  5. Find the derivative of log(sin(logx))

    Text Solution

    |

  6. Find the approximate value of root3(65)

    Text Solution

    |

  7. Verify Rolle's theorem for the function y=f(x)=x^2+4on [-3,3]

    Text Solution

    |

  8. A(2,3) and B(-3,4) be two given points. Find the equation of the locus...

    Text Solution

    |

  9. When the axes are rotated through an angle pi//6. Find the transformed...

    Text Solution

    |

  10. Find the points on the line 3x-4y-1=0 which are at a distance of 5 uni...

    Text Solution

    |

  11. Show that f(x)={{:((cosax-cosbx)/(x^(2))," if " xne0),((1)/(2)(b^(2)...

    Text Solution

    |

  12. Find the derivative of sin2x from the first principles .

    Text Solution

    |

  13. A particle is moving in a straight line so that after 't' seconds its ...

    Text Solution

    |

  14. S.T the tangent at any point theta on the curve x=c sectheta, y=c tan ...

    Text Solution

    |

  15. Find the equation of the straight lines passing through the point (1,2...

    Text Solution

    |

  16. Find the value if k , if the lines joining the origin with the points ...

    Text Solution

    |

  17. If a line makes angles alpha, beta, lambda,delta with the four diagon...

    Text Solution

    |

  18. If x=(3at)/(1+t^(3)),y=(3at^(2))/(1+t^(3)) then find dy/dx.

    Text Solution

    |

  19. At any point t on the curve x=a(t+sint),y=a(1-cost) find the lengths o...

    Text Solution

    |

  20. A wire of length l is cut into two parts which are bent respectively i...

    Text Solution

    |