Home
Class 12
MATHS
If f(x) = {{:(b([x]^(2)+[x])+1",","for",...

If `f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","for",x lt -1):}`, where [x] denotes the integral part of x, then for what values of a, b, the function is continuous at x = - 1?

A

`a=2n+3/2, b epsilon R, n epsilonI`

B

`a=4n+2, b epsilon R, n epsilonI`

C

`a=4n+3/2, b epsilon R^(+), n epsilon I`

D

`a=4n+1, b epsilon R^(+), n epsilon I`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL -1|134 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):} , where [.] and {.} denotes greatest integer and fractional part of x, then

If int_-1^1(sin^-1[x^2+1/2]+cos^-1[x^2-1/2])dx=kpi where [x] denotes the integral part of x , then the value of k is …

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

if f(x)=x^2sin(1/x) , x!=0 then the value of the function f at x=0 so that the function is continuous at x=0

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

The function f(x) = {x} sin (pi [x]) , where [.] denotes the greatest integer function and {.} is the fraction part function , is discontinuous at

For what value of k is the function f(x)={(x^2-1)/(x-1), ,x!=1,k,x=1" continuous at"x=1?

Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

If f(x) = [x] , where [*] denotes greatest integral function. Then, check the continuity on (1, 2]

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL 2
  1. Let function f be defined as f:R^(+)toR^(+) and function g is defined ...

    Text Solution

    |

  2. If f(x)={(2cos x ,s in2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x...

    Text Solution

    |

  3. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  4. Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is different...

    Text Solution

    |

  5. {:(f(x) = cos x and H(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)...

    Text Solution

    |

  6. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |

  7. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  8. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

    Text Solution

    |

  9. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

    Text Solution

    |

  10. Let f (x) be twice differentialbe function such that f'' (x) gt 0 in [...

    Text Solution

    |

  11. Let f:(-pi/2, pi/2)->R, f(x) ={lim(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(t...

    Text Solution

    |

  12. Let f(x+y)=f(x)f(y) for all x, y epsilon R and f(x)=1+x phi (x) l n 2 ...

    Text Solution

    |

  13. Let f(x+y)=f(x)f(y) for all x, y epsilon R and f(x)=1+x phi (x) l n 2 ...

    Text Solution

    |

  14. Let f(x) be a function satisfying f(x+y)=f(x) + f(y) and f(x) = x...

    Text Solution

    |

  15. Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and...

    Text Solution

    |

  16. "If "f(x)+f(y)=f((x+y)/(1-xy))" for all "x,y in R, (xyne1), and under...

    Text Solution

    |

  17. Let f(x) be real valued differentiable function not identically zero s...

    Text Solution

    |

  18. lim(x->oo)(1+a^2)^xsinb/((1+a^2)^x), where a!=0 (a) Both f (x) and g(x...

    Text Solution

    |

  19. If x=int(0)^(y)(dt)/(sqrt(1+9t^(2)))and (d^(2)y)/(dx^(2))=a^(2)y then ...

    Text Solution

    |

  20. Two functions f and g have first and second derivates at x=0 and satis...

    Text Solution

    |