Home
Class 12
MATHS
continuous at x = 0 Let f(x) = {{:((1...

continuous at x = 0
Let `f(x) = {{:((1 + |sin x| )^((a)/(|sin x|)), - (pi)/(6) lt x lt 0 ),(b , x = 0 ),(e^(tan 2x //tan 3x), 0 lt x lt (pi)/(6)):}`
Determine a and b such that f(x) continuous at x = 0 .

A

`p = (1)/(3), q = e^(2//3)`

B

`p = 0, q = e^(2//3)`

C

`p = (2)/(3), q = e^(-2//3)`

D

`p = -(2)/(3), q = e^(2//3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • EAMCET - 2016 AP

    DIPTI PUBLICATION ( AP EAMET)|Exercise Questions|80 Videos

  • ELLIPSE

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 2|1 Videos

Similar Questions

Explore conceptually related problems

f(x) = {{:((1 + |sin x|)^((p)/(|sinx|)) " if " - pi //6 lt x lt 0 ),(e^((sin 2x )/(sin3x) )" if " 0 lt x lt pi //6 ):} and f(0) = q is continuous at x = 0 then

Let f(x) = {:{( sin x +cos x, 0 lt x lt (pi)/(2) ),( a, x = pi//2) , ( tan ^(2) x + cosecx , pi//2lt xlt pi ):} then its odd extension is

For 0 lt x lt (pi)/(2) , prove that cos (sin x) gt sin (cos x) .

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

If 0 lt x lt pi , and cos x+ sin x =1//2 , then tan x=

The larger of sin x+ tan x,2x in 0 lt xlt pi//2 is

DIPTI PUBLICATION ( AP EAMET)-EAMCET - 2016 TS-Questions
  1. If y =a cos (sin x) + b sin (sin x) then y (2) + (tan x) y(1)=

    Text Solution

    |

  2. (d)/(dx) Tan^(-1)[(sqrt(1+sinx) - sqrt(1-sin x))/(sqrt(1+sin x) + sqrt...

    Text Solution

    |

  3. If y = Tan^(-1)[(5 cos - 12 sin x)/(12 cos x + 5 sin x)], then (dy)/(d...

    Text Solution

    |

  4. continuous at x = 0 Let f(x) = {{:((1 + |sin x| )^((a)/(|sin x|)), ...

    Text Solution

    |

  5. lim(x rarr oo)[(x^(2) + x + 3)/(x^(2) - x + 2)]^x =

    Text Solution

    |

  6. The image of the point (5, 2, 6) with respect to the plane x+ y + z = ...

    Text Solution

    |

  7. If the angle betweenthe lines whose direction cosines are (-(2)/(sqrt(...

    Text Solution

    |

  8. Points A(3, 2, 4), B ((33)/(5), (28)/(5), (38)/(5)), and C(9, 8, 10) a...

    Text Solution

    |

  9. Let A (2sec theta, 3 tan theta ) and B( 2sec phi ,3 tan phi ) where t...

    Text Solution

    |

  10. If S and S'' are the foci of the ellipse (x^(2))/(25) + (y^(2))/(16) =...

    Text Solution

    |

  11. For the ellipse given by ((x-3)^(2))/(25) + ((y-2)^(2))/(16) = 1, matc...

    Text Solution

    |

  12. The points of intersection of the parabolas y^(2) = 5x and x^(2) = 5y ...

    Text Solution

    |

  13. From a point (C, 0) three normals are drawn to the parabola y^(2) = x....

    Text Solution

    |

  14. The radical centre of the circles x^(2) + y^(2) = 1, x^(2) + y^(2) - 2...

    Text Solution

    |

  15. If the circles x^(2) + y^(2) - 2lambda x - 2y - 7 = 0 and 3(x^(2) + y^...

    Text Solution

    |

  16. For all real values of k, the polar of the point (2k, k-4) with respec...

    Text Solution

    |

  17. The normal to the circle given by x^(2) + y^(2) - 6x + 8y - 144 = 0 at...

    Text Solution

    |

  18. The piont where the line 4x - 3y + 7 = 0 touches the circle x^(2) + y^...

    Text Solution

    |

  19. The combined equation of three sides of a triangle is (x^(2)-y^(2))(2...

    Text Solution

    |

  20. The equation on the pair of straight lines through the point (1, 1) an...

    Text Solution

    |