Questions asked by Jim S

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• Please help solve this, I can't come up with a solution. The question is to find f? Given `f:(0,+oo)->RR` with `f(x/e)<=lnx<=f(x)-1 , x in (0,+oo)`
  
• How to show that `f` is "1-1" ? (one-to one)
  
• How so I solve this? `2-(x+1)^(1/2)-x^2+4x-3 , 0<x<1`
  
• Domain of `f(x)=ln((x+1))/x` ?
  
• Domain of `f(x)=ln(1+1/x)/x` ?
  
• How to prove that `f` is continuous?
  
• `lim_(xrarr1)sin(π/(x-1))``=`?
  
• Show that `f` has at least one root in `RR` ?
  
• `int_0^1 1/(x^2+1)` `=` ?
  
• Example of a function that doesn't preserve monotonicity?
  
• Find `f` ?
  
• Find `f` ?
  
• Show that `f` has no extremas? (Probably using Fermat's Theorem)
  
• Help with this extrema problem?
  
• Test `f` for concavity?
  
• Show that `|c|<1` ?
  
• Show that `lim_(x to +oo)f'(x)=0` ?
  
• Calculate this integral `int_2^(2sqrt3)1/(x^2sqrt(x^2+4))dx =` ?
  
• Can you think of a different way?
  
• `f'(x_0)=0?` See below.
  
• Show that `int_0^1sinx/sqrt(x^2+1)dx<sqrt2-1` ?
  
• Show that `x/2<``f(x)``<``xf'(x)` , `AAx>0` ?
  
• True or false statement?
  
• Show that `f` is not constant and find `f`?
  
• `int_(-1)^1x^2/(sqrt(x^2+1)+x+1)dx` = ?
  
• True or false?
  
• Solve the equation?
  
• Find `f` ?
  
• Show `|f(b)-f(a)|<= |b-a|` ?
  
• `int_0^pi(xsin^4x)/(sin^4x+cos^4x)dx` = `?`
  
• `int_0^1(x^7-1)/lnxdx` = ?
  
• Show that `|z+1|+|1+z+z^2|+|1+z^3|>=1` ?
  
• Find `int_0^1f(x)dx` ?
  
• Give a small proof of the above?
  
• Prove the following?
  
• Solve `e^x-lnx<=e/x` ?
  
• Show that the ring is commutative?
  
• `lim_(x->0)sin(1/x)/(sin(1/x))` ?
  
• Show that `f` is strictly increasing in `RR` ?
  
• `2-pi/2<=int_0^2f(x)dx<=2+pi/2` ?
  
• Find `f` and 'calculate' the integral?
  
• Check below? (geometry involved)
  
• Find `f` ?
  
• Calculate `lim_(xto1)(e^f(x)-1)/(x-1)` ?
  
• Find the rectangle with the maximum area, which can be turned in the corner. ?