Home
Class 12
MATHS
Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^...

Let ` f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :}` then f(x) is derivable at x =1 , if

A

a=1

B

a=0

C

a =2

D

` a = 1/2 `

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Section -B|35 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Section - C ( More than one options are correct )|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Try youself|16 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):} then f(x) is continuous at x =1 for

Let f(x) = {{:(( 2+x)",",if , x ge0), (( 2-x)",", if , x lt 0):} show that f(x) not derivable at x =0

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

Let f(x)={(tan^(-1)x, , |x|ge1),((x^(2)-1)/4, , |x|lt1):} then domain of f'(x) is

If f(x)={{:(,(x)/(1+|x|),|x|ge 1),(,(x)/(1-|x|),|x| lt 1):} then f(x) is

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Let f(x) = x|x| then f'(0) is equal to

    Text Solution

    |

  2. If f(x) =|x| , then f'(0) is

    Text Solution

    |

  3. Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x)...

    Text Solution

    |

  4. If f(x )=sqrt(25-x^(2)), then what is underset(xto1)lim(f(x)-f(1))/(x-...

    Text Solution

    |

  5. if f(x)=e^(-1/x^2),x!=0 and f (0)=0 then f'(0) is

    Text Solution

    |

  6. If f(x)=log|x|,xne0 then f'(x) equals

    Text Solution

    |

  7. d/(dx) (sin^(-1) "" (2x)/(1+x^(2))) is equal to

    Text Solution

    |

  8. Differential coefficient of log10 x w.r.t logx 10 is

    Text Solution

    |

  9. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

    Text Solution

    |

  10. If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

    Text Solution

    |

  11. If y=ae^(mx)+be^(-mx) then (d^2y)/(dx^2) is

    Text Solution

    |

  12. If y^(2) = ax^(2) + b , " then " (d^(2)y)/( dx^(2))

    Text Solution

    |

  13. If y=(log x)/(x) then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  14. Differentiate the following w.r.t.x. The differentiation coneffiecient...

    Text Solution

    |

  15. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

    Text Solution

    |

  16. If f(x) = cos x cos 2x cos 4x cos (8x). cos 16x then find f' (pi/4)

    Text Solution

    |

  17. If y = cos^(-1)(cos x) then dy/dx at x = (5pi)/4 is (i)1 (ii)-1 (ii...

    Text Solution

    |

  18. If x=e^y+e^((y+ tooo)) , x >0 , then (dy)/(dx) is equal to........

    Text Solution

    |

  19. if x^y . y^x =16 then dy/dx at (2,2) is equal to

    Text Solution

    |

  20. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

    Text Solution

    |