Home
Class 12
MATHS
Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(...

Let `f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0`, test the continuity & differentiability at `x = 0`

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^(p)"sin"1/x,x!=0),(0,x=0):} then f(x) is continuous but not differentiable at x=0 if

If f(x)={xe^(-[(1)/(|x|)+(1)/(x)]);x!=0;0;x=0 Prove that f(x) is not differentiable at x=0

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

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

    Text Solution

    |

  2. Let f(0)=0 and f'(0)=1. For a positive integral k show that lim(x->o) ...

    Text Solution

    |

  3. Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0, test the continuity & ...

    Text Solution

    |

  4. If f(x)= ax^2-b, |x|<1 and f(x)=-1/|x|, |x|>=1 is derivable at x=1 th...

    Text Solution

    |

  5. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

    Text Solution

    |

  6. Discuss the continuity and differentiability in 0,2] of f(x)={|2x-3|...

    Text Solution

    |

  7. Let a1 and a2 be two values of a for which f(x)= x*{ln(1+x)+ln(1-x)}/(...

    Text Solution

    |

  8. Discuss the continuity & the derivability of 'f' where f(x)= degree ...

    Text Solution

    |

  9. Consider the function f(x)=[x^2|cospi/(2x)|\ if\ x!=0 0,\ \ \ \ \ \ ...

    Text Solution

    |

  10. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  11. If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x...

    Text Solution

    |

  12. The integer ' n ' for which (lim)(xvec0)((cos x-1)(cos x-e^x))/(x^n) i...

    Text Solution

    |

  13. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

    Text Solution

    |

  14. Let f: Rvec be such that f(!)=3a n df^(prime)(1)=6. Then ("lim")(xvec...

    Text Solution

    |

  15. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

    Text Solution

    |

  16. If (lim)(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the val...

    Text Solution

    |

  17. If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...

    Text Solution

    |

  18. The function given by y=||x|-1| is differentiable for all real n...

    Text Solution

    |

  19. If |f(x1) - f(x2)| le (x1 - x2)^(2), AA x1 , x2 in R. Find the equatio...

    Text Solution

    |

  20. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |