Home
Class 12
MATHS
Show that the function f(x)={{:((sinx)...

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

Text Solution

Verified by Experts

The correct Answer is:
`a = - (3)/(2), b in R - {0}, c = (1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 4

    ARIHANT PUBLICATION|Exercise Long Answer Type Questions|13 Videos

  • SAMPLE PAPER 4

    ARIHANT PUBLICATION|Exercise Long Answer Type Questions|13 Videos

  • SAMPLE PAPER 3

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS |13 Videos

  • SAMPLE PAPER 5

    ARIHANT PUBLICATION|Exercise Long answer type question|13 Videos

Similar Questions

Explore conceptually related problems

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

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.

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

Show that the function f(x)={{:((e^(1//x)-1)/(e^(1//x)+1)", when "x!=0),(0", when "x=0):} is discontinuous at x=0 .

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.

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)=2x-|x| 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 ?

Show that the function f(x)=1/x is decreasing in (0,oo) .

ARIHANT PUBLICATION-SAMPLE PAPER 4-Short Answer Type Questions
  1. Using properties of determinants, prove the following abs{:(a^2, bc, a...

    Text Solution

    |

  2. Solve the matrix [{:(x,-5,-1):}][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4...

    Text Solution

    |

  3. A coin is tossed once, if it shows head it is tossed again. but if it ...

    Text Solution

    |

  4. If A = [(1,3),(1,4),(1,3)], then verify that A (adj A) = |A|.

    Text Solution

    |

  5. If A and B are two independent events such that P(barAcapB)=2/15 and P...

    Text Solution

    |

  6. Show that y = log (1+ x) - (2x) /( 2+x) , x gt -1 is an increasing fun...

    Text Solution

    |

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

    Text Solution

    |

  8. If y sqrt( 1 - x^(2) ) + x sqrt ( 1 - y^(2) ) = 1, prove that (dy)/( d...

    Text Solution

    |

  9. Prove that the curves y^(2) = 4ax and xy = c^(2) cut at the right angl...

    Text Solution

    |

  10. Using differential find the approximate value of sqrt(0.0037).

    Text Solution

    |

  11. Solve the differential equation (x^(2) - y^(2) ) dx + 2xy dy =0.

    Text Solution

    |

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

    Text Solution

    |

  13. Evaluate int(0)^(pi//3) (sec x . tanx )/( 1+ sec^(2) x) dx.

    Text Solution

    |

  14. Find int ( dx)/( (x-1) (x +1))

    Text Solution

    |

  15. Form the differential equation representing the family of ellipses hav...

    Text Solution

    |

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

    Text Solution

    |

  17. Show that the line (5-x)/(-4) = (y-7)/( 4) = (z+3)/(-5) and (x-8)/( 7)...

    Text Solution

    |

  18. Find the vector equation of the plane through the points (2,1, -1) and...

    Text Solution

    |

  19. Find the points on the line (x+2)/(3) = (y+1)/(2) = (z-3)/(2)  at a d...

    Text Solution

    |

  20. If vecalpha = 3 hat(i) + 4 hat(j) + 5 hat(k) and vecbeta = 2 hat(i) + ...

    Text Solution

    |