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. ?