Home
Class 12
MATHS
What is lim(xto0)(e^(x)-(1+x))/(x^(2)) e...

What is `lim_(xto0)(e^(x)-(1+x))/(x^(2))` equal to?

A

0

B

`(1)/(2)`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto0)lim(e^(x)-(1+x))/(x^(2))`
If we keep `x=0," it is "(0)/(0)`
So, applying L'Hospital role.
`underset(xto0)lim(e^(x)-(1+x))/(x^(2))=(1)/(2)underset(xto0)lim(e^(x)-1)/(x)=(1)/(2)xx1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

What is lim_(xto0)(a^(x)-b^(x))/(x) ?

What is lim_(xto0) e^((1)/(x^(2))) equal to?

lim_(xto0)((e^(x)-1)/x)^(1//x)

What is lim_(xto0) (a^(x)-b^(x))/(x) equal to?

What is lim_(xto0) (2(1-cosx))/(x^(2) equal to?

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

What is lim_(xto0) (sqrt(1+x-1))/(x)

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

    Text Solution

    |

  2. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

    Text Solution

    |

  3. What is lim(xto0)(e^(x)-(1+x))/(x^(2)) equal to?

    Text Solution

    |

  4. The function f:XtoY defined by f(x)=cosx where x""inX, is one-one and ...

    Text Solution

    |

  5. If f(x)=(x)/(x-1), then what is (f(a))/(f(a+1)) equal to?

    Text Solution

    |

  6. Let f:[-6,6]toR be defined by f(x)=x^(2)-3. Consider the following : ...

    Text Solution

    |

  7. Let f(x)=px+qandg(x)=mx+n." Then "f(f(x))=g(f(x)) is equivalent to

    Text Solution

    |

  8. If F(x)=sqrt(9-x^(2)), then what is lim(xto1) (F(x)-F(1))/(x-1) equal ...

    Text Solution

    |

  9. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

    Text Solution

    |

  10. Let f(x) be defined as follows : f(x)={{:(2x+1",",-3ltxlt-2),(x-1","...

    Text Solution

    |

  11. Consider the following statements : 1. If lim(xtoa) f(x) and lim(xto...

    Text Solution

    |

  12. Let f(a)=(a-1)/(a+1) Consider the following : 1. f(2a)=f(a)+1 2....

    Text Solution

    |

  13. Suppose the function f(x)=x^(n),n!=0 is differentiable for all x. Then...

    Text Solution

    |

  14. The inverse of the function y=5^(Inx) is

    Text Solution

    |

  15. A function is defined as follows : f(x)={{:(-(x)/(sqrtx^(2))",",xne0...

    Text Solution

    |

  16. Consider the following : 1. x+x^(2) is continuous at x=0 2. x+cos(...

    Text Solution

    |

  17. A function is defined in (0,oo) by f(x)={{:(,1-x^(2)," for ",0ltxle1...

    Text Solution

    |

  18. Consider the following statements : 1. Derivative of f(x) may not ex...

    Text Solution

    |

  19. The function f(x)=|x|-x^(3) is

    Text Solution

    |

  20. If l(1)=(d)/(dx)(e^(sinx)) l(2)lim(hto0) (e^(sin(x+h))-e^(sinx))/(h)...

    Text Solution

    |