Home
Class 12
MATHS
The function f(x)={(x^2/a, if 0le x lt1)...

The function `f(x)={(x^2/a, if 0le x lt1),(a, if 1 le x lt sqrt2),((2b^2-4b)/(x^2), if sqrt(2) le xlt oo):}` is continuous on `[0,oo)dot` Find the most suitable values of `a` and `bdot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

The function f(x)={x^2a a,if1lt=x

The function f(x)= {{:(,x^(2)//a,0lexlt1),(,a,1lexltsqrt2),(,(2b^(2)-4b)/(x^(2)),sqrt2le xltoo):} and if it is continous at x=1, sqrt2 , then a and b is equal to

The function f(x)={{:(,(x^(2))/(a),0 le x lt 1),(,a,1le x lt sqrt2),(,(2b^(2)-4b)/(x^(2)),sqrt2 le x lt oo):} is a continuous for 0 le x lt oo . Then which of the following statements is correct?

Let a , b in R,(a in 0) . If the funtion f defined as f(x)={{:(,(2x^(2))/(a),0 le x lt 1),(,a,1 le x lt sqrt2),(,(2b^(2)-4b)/(x^(3)),sqrt2lt x lt oo):} is a continous in [0,oo) . Then, (a,b)=

The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

Given fuction, {(x^(2), "for" 0 le x lt1),(sqrtx, "for" 1le x le 2):} Evaluate int_(0)^(2) f(x) d x .

Given fuction, {(x^(2), "for" 0 le x lt1),(sqrtx, "for" 1le x le 2):} Evaluate int_(0)^(2) f(x) d x .

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

The function f(x) ={{:( 5x-4, " for " 0 lt x le 1) ,( 4x^(2) - 3x, " for" 1 lt x lt 2 ),( 3x + 4 , "for" x ge2):}is

RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. If f(x)={e^(1/x) ,1 ifx!=0ifx=0 Find whether f is continuous a...

    Text Solution

    |

  2. Test the continuity of the following function at the origin; f(x)={x...

    Text Solution

    |

  3. The function f(x)={(x^2/a, if 0le x lt1),(a, if 1 le x lt sqrt2),((2b^...

    Text Solution

    |

  4. A function f(x) is defined as f(x)={(x^2 -x-6)/(x-3);ifx!=3 and 5ifx=...

    Text Solution

    |

  5. Find the domain of f(x) = sin^-1 x+ cos x

    Text Solution

    |

  6. If y=(x-1)log(x-1)-(x+1)log(x+1), prove that : dy/dx = log((x-1)/(1+x)...

    Text Solution

    |

  7. The value of f(0) , so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

    Text Solution

    |

  8. The value of a for which the function f(x) = {[5x-4,if 0ltxle1],[4x^2...

    Text Solution

    |

  9. Evaluate : tan(cos^-1(-7/25))

    Text Solution

    |

  10. The function f(x)=tanx is discontinuous on the set {npi; n in Z} (b)...

    Text Solution

    |

  11. If f(x)=|(log)(10)x| , then at x=1 f(x) is continuous and f^(prime)(1...

    Text Solution

    |

  12. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

    Text Solution

    |

  13. If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a...

    Text Solution

    |

  14. If f(x)={m x+1,xlt=pi/2sinx+n ,x >pi/2 is continuous at x=pi/2, t...

    Text Solution

    |

  15. If f(x)={((36^x-9^x-4^x+1)/(sqrt(2)-sqrt(1+cosx)),x!=0),(k ,x=0)) is ...

    Text Solution

    |

  16. If f(x)={(1-cos10x)/(x^2a),x<0(sqrt(x))/(sqrt(625)+sqrt(x)-25),x >0,x=...

    Text Solution

    |

  17. If f(x)={((sin(cosx)-cosx)/((pi-2x)^2) ,, x!=pi/2),(k ,, x=pi/2):} is ...

    Text Solution

    |

  18. Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx...

    Text Solution

    |

  19. The value of a for which the function f(x)={(((4^x-1)^3)/(sin(x/a)log...

    Text Solution

    |

  20. If f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,1ltxge2)) then the value of(a...

    Text Solution

    |