Home
Class 12
MATHS
Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"i...

Let `f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2)),"if "x gt(pi)/(2)):}" ,"`
if f (x) is continuous at `x=(pi)/(2)` , find a and b .

Text Solution

Verified by Experts

The correct Answer is:
`a=-1/2 , b=4`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILTY

    CBSE COMPLEMENTARY MATERIAL|Exercise 2 Marks Questions|20 Videos

  • APPLICATIONS OF INTEGRALS

    CBSE COMPLEMENTARY MATERIAL|Exercise FOUR/SIX MARK QUESTIONS|26 Videos

  • DIFFERENTIAL EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise SIX MARK QUESTIONS|4 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2))",",x gt (pi)/(2)):} is continuous at x=(pi)/(2) , then the value of ((b)/(a))^(5//3) is

Let f(x)={(1-s in^3x)/(3cos^2x) , if x pi/2 . If f(x) is continuous at x=pi/2 , find a and b .

f(x)={(sin(cos x)-cos x)/((pi-2x)^(3)),quad if x+-(pi)/(2) and k,quad if x=(pi)/(2) is continuous at x=(pi)/(2), then k

Determine a & b so that f is continuous at x = pi/2 whre f(x) = [{:((1-sin^(3)x)/(3 cos^(2)x), if, x lt pi/2),(a, if, x=pi/2),((b(1-sinx))/(pi-2x)^(2), if, x gt pi/2):}

If f(x) = {(ax+1,",",x le (pi)/(2)),(sin x+ b,",",x gt (pi)/(2)):} is continuous at x = (pi)/2 , then

If f(x)={{:((1-sinx)/(pi-2x),,","xne(pi)/(2)),(lambda,,","x=(pi)/(2)):},"be continuous at "x=(pi)/(2), then value of lambda is

If f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):} is continuous at x= pi/2 , where , then k=

If : f(x) {: ((1-sin x)/(pi-2x)", ... " x != pi//2 ),(=lambda ", ... " x = pi//2):} is continuous at x = pi//2 , then : lambda =

CBSE COMPLEMENTARY MATERIAL-CONTINUITY AND DIFFERENTIABILTY-4 Marks Questions
  1. Determine the values of a ,\ b ,\ c for which the function f(x)={(s...

    Text Solution

    |

  2. f(x)={{:(,[x]+[-x], x ne 0),(,lambda,x=0):} Find the value of lambda...

    Text Solution

    |

  3. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

    Text Solution

    |

  4. If f(x)={x^2+3x+a ,xlt=1b x+2,forx >1 is everywhere differentiable, f...

    Text Solution

    |

  5. Find the realtionship between a and b so that the function defined by ...

    Text Solution

    |

  6. Differentiate tan^(-1)((sqrt(1-x^(2)))/(x)) w.r.t. cos^(-1)(2xsqrt(1-x...

    Text Solution

    |

  7. If y=x^(x^(x)), "then find "(dy)/(dx).

    Text Solution

    |

  8. Differentiate (x cos x)^(x)+(x sin x)^(1/x) w.r.t.x.

    Text Solution

    |

  9. If x^m y^n=(x+y)^(m+n) , prove that (dy)/(dx)=y/x .

    Text Solution

    |

  10. If (x-y)dot(x-y)/x=a , Prove that y(dy)/(dx)+x=2ydot

    Text Solution

    |

  11. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

    Text Solution

    |

  12. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  13. Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"w i t hr e s p e...

    Text Solution

    |

  14. If sqrt(1-x^6)+sqrt(1-x^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2)...

    Text Solution

    |

  15. If f(x)=sqrt(x^2+1),\ \ g(x)=(x+1)/(x^2+1) and h(x)=2x-3 , then find f...

    Text Solution

    |

  16. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

    Text Solution

    |

  17. If x^(y)+y^(x)+x^(x)=m^(n)." then find the value of "(dy)/(dx).

    Text Solution

    |

  18. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

    Text Solution

    |

  19. If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin ...

    Text Solution

    |

  20. If x^(2)/a^(2)+y^(2)/b^(2)=1" then show that "(d^(2)y)/(dx^(2))=-b^(4)...

    Text Solution

    |