Home
Class 12
MATHS
Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(...

Let `f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):}` If f(x) is continuous and differentiable at any point, then values of a and b are

A

`(-1)/(2),(3)/(2)`

B

`(1)/(2), (-3)/(2)`

C

`(1)/(2), (3)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = {:(1/(x^2) , : |x| ge 1),(alphax^2 + beta , : |x| < 1):} . If f(x) is continuous and differentiable at any point, then

Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is continuous and differentiable at any point, then (A) a=1/2, b=-3/2 (B) a=-1/2, b=3/2 (C) a=1,b=-1 (D) none of these

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

Let f(x)={{:(3x^(2)-4sqrtx+1,"for",xlt1),(ax+b,"for",xge1):} If f(x) is continuous and differentiable for all real values in its domain then

Let f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x) is continuous and differentiable at any point, then a=1/2,b=-3/2 (b) a=-1/2,b=3/2 a=1, b=-1 (d) none of these

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Let f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2)).sin^(-1)(1-{x}))/(sqrt(2)...

    Text Solution

    |

  2. Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2...

    Text Solution

    |

  3. Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If...

    Text Solution

    |

  4. If f(x) = {{:(A+Bx^(2)",",x lt 1),(3Ax - B+2",",x ge 1):}, then A and ...

    Text Solution

    |

  5. If f(x) = {{:(|x-1|([x]-x)",",x ne 1),(0",",x = 1):}, then

    Text Solution

    |

  6. If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):}, where [.] an...

    Text Solution

    |

  7. If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):}, then g(x)...

    Text Solution

    |

  8. If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(...

    Text Solution

    |

  9. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

    Text Solution

    |

  10. Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...

    Text Solution

    |

  11. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  12. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

    Text Solution

    |

  13. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

    Text Solution

    |

  14. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  15. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  16. f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)

    Text Solution

    |

  17. If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, t...

    Text Solution

    |

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

    Text Solution

    |

  19. Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  20. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |