Home
Class 12
MATHS
If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(...

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

A

continous at x=0

B

discontinuous at x=0

C

`f(0)=1`

D

L.H.L.=0

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL 2|103 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|14 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos
  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

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

f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):} at x = 0

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

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):} , then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)

If f(x)={{:((e^((2)/(x))-1)/(e^((2)/(x))+1),:,x ne 0),(0,:,x=0):} , then f(x) is

The value of k for which f(x)={{:(,[1+x(e^(-1//x^(2)))sin(1/(x^(4)))]^(e^(1//x^(2))),x ne 0),(,k,x=0):} is continuous at x=0, is

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

Check the continuity of f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):}at x = 0

If f(x)= {{:(,(1)/(x)-(2)/(e^(2x)-1),x ne 0),(,1,x=0):}

If f(x)={{:(,(e^(x[x])-1)/(x+[x]),x ne 0),(,1,x=0):} then

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Let f(x)={(x^2,x notin Z),((k(x^2-4))/(2-x),x notinZ):} Then, lim(xt...

    Text Solution

    |

  2. If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxl...

    Text Solution

    |

  3. If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(e^(1//x)+e^(1//x)))",",x ne 0)...

    Text Solution

    |

  4. If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is continuous at x=0, ...

    Text Solution

    |

  5. If f(x)=(sin3x+Asin2x+Bsinx)/(x^(5)) forx!=0 is continuous at x=0, the...

    Text Solution

    |

  6. If f(x)={((a^(2[x]+{x})-1)"/ "(2[x]+{x}),x!=0),(log(e)a,x=0):} Then ...

    Text Solution

    |

  7. Let [] donots the greatest integer function and f (x)= [tan ^(2) x], t...

    Text Solution

    |

  8. f(x)=[tan^(-1)x] where [.] denotes the greatest integer function, is d...

    Text Solution

    |

  9. f(x)=[sinx] where [.] denotest the greatest integer function is contin...

    Text Solution

    |

  10. if f(x) = tan(pi[(2x-3pi)^3])/(1+[2x-3pi]^2) ([.] denotes the greates...

    Text Solution

    |

  11. The jump value of the function at the point of the discontinuity of th...

    Text Solution

    |

  12. Solve (1-x)dy=e^y dx

    Text Solution

    |

  13. The value of f(0), so that the function f(x)=(1-cos(1-cosx))/(x^(4...

    Text Solution

    |

  14. If lim(xtoa^(+))f(x)=l=lim(xtoa^(-))g(x) and lim(xtoa^(-))f(x)=m=lim(x...

    Text Solution

    |

  15. Solve ydx=(1+x^2)dy

    Text Solution

    |

  16. f+g may be a continuous function, if (a) f is continuous and g is disc...

    Text Solution

    |

  17. The value of f(0) such that f(x)=((1+tanx)/(1+sinx))^(cosecx) can be m...

    Text Solution

    |

  18. The inverse of the function f:Rto range of f, defined by f(x)=(e^(x)-e...

    Text Solution

    |

  19. If f(x)={((sin([x]+x))/([x]+x),x!=0),(1,x=0):} when [.] denotes the gr...

    Text Solution

    |

  20. In x epsilon(0,1),f(x)=[3x^(2)+1], where [x] stands for the greatest i...

    Text Solution

    |