Questions asked by Mr.X

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• How do you prove if #lim_(n->infty) x_(2n) = L = lim_(n->infty) x_(2n+1)#, then #lim_(n->infty) x_n = L#?
  
• Does #sum_(n=1)^oo 3^n/(n!)# converge ?
  
• Dose #sum ((n^2+3)/(2+n^2))^(n^3)# with #n = 0 -> # infinity converge ?
  
• How do you prove this ? if #lim_(n->oo)x_(2n)=L=lim_(n->oo)x_(2n+1)# then #lim_(n->oo)x_(n)=L#
  
• How do you prove this ? #sum_(n=1)^oo a_n# converges #-># #sum_(n=1)^oo a_n^2# converges
  
• How do you find this ? #lim_(x->0)sum_(n=1)^oo(cosnx)/((4n-3)(4n+1))#
  
• Prove or disprove ? #f(A/B)=f(A)/f(B)#
  
• What dose #{x_n}# converges ? when #x_1=5/2,5x_(n+1)=x_n^2+6#
  
• How do you solve this ? #lim_(x->0^+)(1+sin(4x))^cot(x)#
  
• How do you find #m# when #mZZ=<-10,8,26># ? (Abstract algebra)
  
• How do you find ? #lim_(x->0)int_(0)^(2x)(e^(t^2))/(x+tan(x))#
  
• If #f:[0,1]->RR,|f'(x)|<1# how do you show #f(1/n)# converges ?
  
• Let #f:[a,b]->RR, f# integrate and converges at #x_0# #F:[a,b]->RR,##F(x)=int_a^xf(t)dt# how do you show #F# differentiable at #x_0# ?
  
• How do you prove #log_2 3# is irrational number ?
  
• How to prove or dis prove ? #if lim_(x->a)f(x)=b and lim_(x->b)g(x)=c# then #lim_(x->a)g๐f(x)=c#
  
• How to prove or disprove ? if #f# is integrable on #[a,b]# then #int_a^b|f(x)|dx<=|int_a^bf(x)dx|#
  
• If #A_x=(-1/(x^2+1),1/(|x|+1)]# how do you find ? #uuu_(x=1)^(oo)A_x= ?# and #nnn_(x=1)^(oo)A_x=?#
  
• Let #G# be a group and #H# be a subgroup of#G=<a># if#|G|=36#and#H=<a^4>#. How do you find #|H|# ?
  
• Let #G# is cyclic group and #|G|=48#. How do you find all of subgroup of #G# ?
  
• If #H# and #K# is subgroup of #G# and #|H|=10,|K|=49# then how do you find #|HnnK|# ?
  
• #f# is a function on real where #f(x)=2x^2-x# How do you find #f^-1(x)# ?
  
• #f# is a function on #RR# where #f(x)=|x^2-2|#, How do you find #f^-1(x)#?
  
• Does #sum_(n=2)^oo1/(nln(n))# converges ?
  
• Let #f:[a,b]->RR^+uu{0}# where #int_0^bf(x)dx=0# then #f(x)=0# on #[a,b]# this sentence true or false ?
  
• How to find #int((1)/(x-sqrt(x+2)))dx# ?
  
• How to find #dy/dx# from #x^2y+3xy^2-x=5#?
  
• How to find #lim_(x->oo)1/(|x|+1)# ?
  
• How to prove this ? #2|k^2# then #2|k# for some #k\inZZ#
  
• How to prove this ? if #7|k^2# then #7|k# for some #k\inZZ#
  
• Help plz ! we say that 1) #x\inuuu_(n\inN)A_n# if #x\inA_n# for some #n\inN# and 2)#x\innnn_(n\inN)A_n# if #x\inA_n# for all #n\inN# prove or dispprove #nnn_(n\inN)A_n\sube uuu_(n\inN)A_n# for any index set #N# ?
  
• Please, give me an example #f:NNxxNN\toNN# #f# is a bijection ?