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 ?