Home
Class 12
MATHS
Let a , b in R,(a in 0). If the funtion ...

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)=

A

`(-sqrt2,1-sqrt3)`

B

`(sqrt2,-1+sqrt3)`

C

`(sqrt2,1+sqrt3)`

D

`(-sqrt2,1+sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Paper|12 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Exercise (Numerical Answer)|16 Videos

  • JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )

    MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

Let a , b in R,(a ne 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)={{:(,(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?

If f(x)={{:(,4,-3lt x lt -1),(,5+x,-1le x lt 0),(,5-x,0 le x lt 2),(,x^(2)+x-3,2 lt x lt 3):} then, f(|x|) is

If f(x) {:(=x^(2)/a", if " 0 le x lt 1 ),(= a", if " 1 le x lt sqrt(2) ),(=(2b^(2)-4b)/(x^(2))", if " sqrt(2) le x ) :} is continuous in (0,oo) , then the most suitable values of a and b ( in that order ) are

Let f: R to R be a function defined as f(x)={(,(sin (a+1)x+sin 2x)/(2x), if x lt 0),(, b, if x=0), (,(sqrt(x+bx^(3))-sqrtx)/(bx^(5/2)), if x gt 0):} If f is continuous at x=0 then the value of a+b is equal to :

If f(x) {:(=x^(2)+ax+b", if "0 le x lt 2 ),(= 3x+2", if " 2 le x le 4 ),(=2ax + 5b ", if " 4 lt x le 8 ) :} is continuous on [ 0,8] then a-b = ……

Let f (x) be defined as f (x) ={{:(|x|, 0 le x lt1),(|x-1|+|x-2|, 1 le x lt2),(|x-3|, 2 le x lt 3):} The range of function g (x)= sin (7 (f (x)) is :

Find the inverse of each of the following functions : f(x) = {{:(x"," -oo lt x lt 1),(x^(2)"," 1 le x le 4),(2x"," 4 lt x lt oo):}

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Questions for Previous Years AIEEE/JEE Main Papers
  1. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

    Text Solution

    |

  2. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

    Text Solution

    |

  3. Let a , b in R,(a in 0). If the funtion f defined as f(x)={{:(,(2x^(...

    Text Solution

    |

  4. Lim( x -> 0) (1 -cos2x)^2 / (2xtanx - x tan2x) is

    Text Solution

    |

  5. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

    Text Solution

    |

  6. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

    Text Solution

    |

  7. lim(x->3) (sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) is equal to

    Text Solution

    |

  8. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  9. The value of lim(xto pi//2)(cot x-cosx)/(pi-2x)^3 is

    Text Solution

    |

  10. For each t in R let [t] be the greatest integer less than or equal to ...

    Text Solution

    |

  11. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

    Text Solution

    |

  12. lim(x-gt0)((27+x)^(1/3)-3)/(9-(27+x)^(2/3))

    Text Solution

    |

  13. If the function f defined as f(x) = 1/x - (k-1)/(e^(2x)-1), x != 0, is...

    Text Solution

    |

  14. lim(y->oo)(sqrt(1+sqrt(1+y^(4)))-sqrt(2))/(y^(4))= (a) (1)/(4sqrt...

    Text Solution

    |

  15. For each x in R, let [x] be the greatest integer less than or equal t...

    Text Solution

    |

  16. For each t in RR, let [t] be the greatest integer less than or equal t...

    Text Solution

    |

  17. Let [x] denote the greatest integer less than or equal to Then: li...

    Text Solution

    |

  18. underset(x to 0) lim(x cot(4x))/(sin^(2) x cot^(2)(2x)) is equal to

    Text Solution

    |

  19. underset(xto pi/4)lim(cot^3x-tanx)/(cos(x+pi/4)) is

    Text Solution

    |

  20. underset(x to 1-)lim (sqrtpi-sqrt(2 sin^(-1) x))/sqrt(1-x) is equal t...

    Text Solution

    |