Home
Class 12
MATHS
Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2d...

Let `f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")_(xvec1)f(x)e xi s t s ,t h e nai s` 1 (b) `-1` (c) 2 (d) `-2`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos

  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

Let f(x)={{:(,sin2x,0 lt x le xpi//6),(,ax+b,pi//6 lt x lt 1):} If f(x) and f'(x) are continuous, then

Let f(x)={(-1, -2 leq x lt 0),(x^2-1, 0 lt x leq 2)) and g(x)= |f(x)|+f|x| then the number of points which g(x) is non differentiable, is (A) at most one point (B) 2 (C) exactly one point (D) infinite

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

Let f(x)={{:(,3^x,at,-1lt x lt0),(,4,at,0 le x lt 1),(,3x-1, at,1 le x le 3):} Find f(2), f(0), f(0.5), f(-0.5), f(3).

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous ...

    Text Solution

    |

  2. Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha ...

    Text Solution

    |

  3. Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")(xvec1)f(x)e xi s t...

    Text Solution

    |

  4. Given a real valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

    Text Solution

    |

  5. Which of the following statement(s) is (are) INCORRECT ?. (A) If lim...

    Text Solution

    |

  6. Each question contains statements given in two columns which have to b...

    Text Solution

    |

  7. If L=+(lim)(x->1)((2x-3)(sqrt(x)-1))/(2x^2+x-3),\ t h e n\ 20\ L=

    Text Solution

    |

  8. If L=(lim)(x->oo)(logx^n-[x])/([x]),\ w h e r e\ n in N ,\ t h e n-2L...

    Text Solution

    |

  9. (lim)(x->0)([100(sin x)/x]+[100(tanx)/x])=

    Text Solution

    |

  10. (lim)(x->0)([100 x/(sin\ x)]+[100(tanx)/x])=

    Text Solution

    |

  11. (lim)(x->0)([100(sin^(-1)\ x)/x]+[100(tan^(-1)x)/x])=

    Text Solution

    |

  12. (lim)(x->0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x])=

    Text Solution

    |

  13. lim(x -> oo) (sqrt(x^2 - x - 1) - ax - b) = 0 where a > 0, then there ...

    Text Solution

    |

  14. If lim(x->oo)((1+a^3)+8e^(1/ x))/(1+(1-b^3)e^(1/ x))=2, then there exi...

    Text Solution

    |

  15. If (lim)(x->oo)(sqrt((x^4-x^2+1))-a x^2-b)=0 , then there exists at ...

    Text Solution

    |

  16. If lim(x->-a) (x^7+a^7)/(x+a)=7, where a lt 0 then ,there exists at ...

    Text Solution

    |

  17. (lim)(x->\ oo)(x/(1+x))^x equals

    Text Solution

    |

  18. (lim)(x->\ oo)(sin1/x+cos1/x)^x equals

    Text Solution

    |

  19. (lim)(x->\ 0)(cosx)^(cot2x) equals

    Text Solution

    |

  20. Evaluate the following limit: (lim)(x->pi/4)(1-t a n x)/(x-pi/4)

    Text Solution

    |