Home
Class 12
MATHS
If f(x)={((1+2x)^(1//x)",","for " x ne 0...

If `f(x)={((1+2x)^(1//x)",","for " x ne 0),(e^(2)",", "for " x =0):}`, then

A

`lim_(x to 0^(+))f(x)=e`

B

`lim_(x to 0)f(x) = e^(2)`

C

f(x) is discontinuous at x = 0

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `f(x) ={((1+2x)^(1//x)",",x ne 0),(e^(2)",",x =0):}`
Now, ` lim_( x to 0) f(x) =lim_( x to 0)(1+2x)^(1//x) = lim_( x to 0) [ (1+2x)^((1)/(2x))]^(2) =e^(2)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

If f(x)={:{((e^(1/x)-1)/(e^(1/x)+1)", for " x !=0),(1", for " x=0):} , then f is

IF f(x) = {{:( (1)/(2) sin ^(2) x , "for " x ne 0 ),( 0,"for " x=0 ):},then at x=0

The function f given by f(x)={((e^(1//x)-1)/(e^(1//x)+1)",","if",x ne 0),(0",","if", x =0):} , is

If f(x)={((1)/(1+e^(1//x))"," ,x ne 0),(0",", x =0):} then f(x) is :

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable

If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} then f(x) is

Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", " x= 0):}, at x=0.

For the function f (x) = {{:(x/(1+e^(1//x))", " x ne 0),(" 0 , "x = 0):} , the derivative from the right, f'(0^(+)) = … and the derivative from the left, f'(0^(-)) = … .

If f(x)={(e^((1)/(x))/(1+e^((1)/(x)))",", x ne0),(0",",x=0):} , then

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. if f(x) is continuous and f(9/2)=2/9 then the value if lim(x->0)f((1-c...

    Text Solution

    |

  2. If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...

    Text Solution

    |

  3. If f(x)={((1+2x)^(1//x)",","for " x ne 0),(e^(2)",", "for " x =0):}, t...

    Text Solution

    |

  4. If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...

    Text Solution

    |

  5. If f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):} then f(x) is

    Text Solution

    |

  6. For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...

    Text Solution

    |

  7. If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)...

    Text Solution

    |

  8. Which of the following functions is continuous at x = 0 ?

    Text Solution

    |

  9. For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...

    Text Solution

    |

  10. For what value of k, f(x)={((2^(x+2)-16)/(4^(x)-16)",", x ne 2),(k",",...

    Text Solution

    |

  11. For what value of k, the function f(x)={((x)/(|x|+2x^(2))",", x ne 0)...

    Text Solution

    |

  12. The points of discontinuity of the function lim(n->oo) (((2 sin x )^(2...

    Text Solution

    |

  13. The function f(x)=(sin 2x)^(tan^(2)2x) is not defined at x=(pi)/(4). T...

    Text Solution

    |

  14. If the function f as defined below is continuous at x=0find the values...

    Text Solution

    |

  15. If a function y=f(x) is defined as y=(1)/(t^(2)-t-6)and t=(1)/(x-2), t...

    Text Solution

    |

  16. Let f(x)={((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2)"," , x ne 0),(a",",...

    Text Solution

    |

  17. Let f(x)={(1-cos4x)/(x^2),\ \ \ if\ x<0a ,\ \ \ if\ x=0(sqrt(x))/(sqrt...

    Text Solution

    |

  18. lim(x->pi/2) ((1-tan(x/2))(1-sinx))/((1+tan(x/2))((pi-2x)^3))

    Text Solution

    |

  19. If f(x)=(sin 2x+A sinx+B cosx)/(x^(3)) is continuous at x = 0, then t...

    Text Solution

    |

  20. f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","...

    Text Solution

    |