Bài 15 giải như thế nào nhỉ! Giải theo phương pháp nhân t vào một vế thì ra, nhưng còn cách đặt ẩn phụ a, b thì làm ra sao?

Có cách nào chỉnh tiêu đề không? Mình đánh Latex trên tiêu đề nhưng nó không hiện!

$\lim_{x\rightarrow +\infty}x^{2}\left ( \frac{e^{\frac{1}{x^{2}}}-\cos \frac{1}{x}}{\arctan x} \right )$

$\begin{align*} \lim_{x\to+\infty}x^{2}\cdot \left ( \dfrac{e^{\tfrac{1}{x^{2}}}-\cos\frac{1}{x}}{\arctan x} \right )&=\lim_{x\to+\infty}\left (x^2\cdot \dfrac{e^{\tfrac{1}{x^{2}}}-1+1-\cos\frac{1}{x}}{\pi/2}  \right )\\&=\lim_{x\to+\infty}\left (x^2\cdot\frac{1/{x^2}+\frac12\cdot 1/{x^2}}{\pi/2}  \right )\\&=\frac3\pi \end{align*}$

L= $\lim_{x \to \infty } ( 1+ \tfrac{3x+2}{2x^{2}+x-1} )^{2x}$

giúp mình bài này nhé ! 

\begin{align*} \lim_{x \to \infty }  \left ( 1+ \frac{3x+2}{2x^{2}+x-1} \right )^{2x}&=\lim_{x \to \infty } \left ( 1+ \frac{3x+2}{2x^{2}+x-1}\right )^{\tfrac{{2x^{2}+x-1}}{3x+2}\cdot 2x\cdot\tfrac{3x+2}{2x^{2}+x-1}}\\&=e^{\lim\limits_{x\to\infty}\left (2x\cdot\tfrac{3x+2}{2x^{2}+x-1} \right )}\\&=e^3 \end{align*}

Xin lỗi nhưng em thử luôn

*** Cannot compile formula:


 
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
 
\clip(0.20977489984620393,-1.1493373302552163) rectangle (8.333146325376696,3.493696528421076);
 
\draw [shift={(2.,0.)},color=ffqqqq,fill=ffqqqq,fill opacity=0.1] (0,0) -- (0.:0.23253925836442244) arc (0.:36.86989764584402:0.23253925836442244) -- cycle;
 
\fill[color=zzttqq,fill=zzttqq,fill opacity=0.1] (2.,0.) -- (6.,3.) -- (6.,0.) -- cycle;
 
\draw [color=zzttqq] (2.,0.)-- (6.,3.);
 
\draw [color=zzttqq] (6.,3.)-- (6.,0.);
 
\draw [color=zzttqq] (6.,0.)-- (2.,0.);
 
\draw (3.372308813602349,1.7496520906879116) node[anchor=north west] {$\sqrt{a^2+b^2}$};
 
\begin{scriptsize}
 
\draw [fill=qqqqff] (6.,0.) circle (1.5pt);
 
\draw[color=qqqqff] (6.108520753690387,0.021110270179041365) node {$C$};
 
\draw [fill=qqqqff] (6.,3.) circle (1.5pt);
 
\draw[color=qqqqff] (6.0542615934053545,3.1061310978137064) node {$B$};
 
\draw [fill=qqqqff] (2.,0.) circle (1.5pt);
 
\draw[color=qqqqff] (1.8840575600700453,0.14513120797339976) node {$A$};
 
\draw[color=ffqqqq] (2.4111465456960692,0.14513120797339976) node {$\varphi$};
 
\draw[color=zzttqq] (6.085266827853944,1.4861075978748999) node {$a$};
 
\draw[color=zzttqq] (4.085429205919912,-0.11841328483961183) node {$b$};
 
\end{scriptsize}
 
 
\end{tikzpicture}


*** Error message:
Error: Nothing to show, formula is empty

Hình xấu thật. Nhưng mà sau mỗi dòng lệnh phải cách nhau 1 dòng trống phải không anh? Em để nguyên mã xuất ra từ GeoGebra thì diễn đàn báo lỗi "Not allowed the command sequence" gì đó.

*** Cannot compile formula:



\definecolor{qqwuqq}{rgb}{0.,0.39215686274509803,0.}
\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
\definecolor{zzttqq}{rgb}{0.6,0.2,0.}
\definecolor{qqqqff}{rgb}{0.,0.,1.}
 
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(1.0660964319724329,-2.4651239327570766) rectangle (8.430743931744104,5.210158962435522);
\fill[color=zzttqq,fill=zzttqq,fill opacity=0.1] (3.7970992833816113,4.65360387897299) -- (1.1825847052552894,-0.25184674038281973) -- (8.366028224364738,-0.25184674038281973) -- cycle;
\draw[color=qqwuqq,fill=qqwuqq,fill opacity=0.1] (2.1675449400363203,1.596172710023169) -- (2.4098439958456805,1.4670317884572301) -- (2.5389849174116197,1.70933084426659) -- (2.2966858616022594,1.8384717658325291) -- cycle; 
\draw[color=qqwuqq,fill=qqwuqq,fill opacity=0.1] (5.890594289319993,2.003065863202262) -- (6.077727468248967,1.8021495039555742) -- (6.278643827495655,1.9892826828845478) -- (6.091510648566681,2.1901990421312356) -- cycle; 
\draw[color=qqwuqq,fill=qqwuqq,fill opacity=0.1] (4.470142640127001,0.022718752840577505) -- (4.195577146903604,0.02271875284057756) -- (4.195577146903604,-0.2518467403828197) -- (4.470142640127001,-0.25184674038281973) -- cycle; 
\draw [color=zzttqq] (3.7970992833816113,4.65360387897299)-- (1.1825847052552894,-0.25184674038281973);
\draw [color=zzttqq] (1.1825847052552894,-0.25184674038281973)-- (8.366028224364738,-0.25184674038281973);
\draw [color=zzttqq] (8.366028224364738,-0.25184674038281973)-- (3.7970992833816113,4.65360387897299);
\draw (4.470142640127001,0.6800594458800253)-- (4.470142640127001,-0.25184674038281973);
\draw (4.470142640127001,0.6800594458800253)-- (2.2966858616022594,1.8384717658325291);
\draw (4.470142640127001,0.6800594458800253)-- (6.091510648566681,2.1901990421312356);
\draw (1.1825847052552894,-0.25184674038281973)-- (6.091510648566681,2.1901990421312356);
\draw (2.2966858616022594,1.8384717658325291)-- (8.366028224364738,-0.25184674038281973);
\draw (4.470142640127001,-0.25184674038281973)-- (3.7970992833816113,4.65360387897299);
\draw (2.2966858616022594,1.8384717658325291)-- (6.091510648566681,2.1901990421312356);
\draw (6.091510648566681,2.1901990421312356)-- (4.470142640127001,-0.25184674038281973);
\draw (2.2966858616022594,1.8384717658325291)-- (4.470142640127001,-0.25184674038281973);
\begin{scriptsize}
\draw [fill=qqqqff] (1.1825847052552894,-0.25184674038281973) circle (1.5pt);
\draw[color=qqqqff] (1.14375528082767,-0.0706427597205999) node {$A$};
\draw [fill=qqqqff] (3.7970992833816113,4.65360387897299) circle (1.5pt);
\draw[color=qqqqff] (3.8877012737127212,4.83480785963521) node {$B$};
\draw [fill=qqqqff] (8.366028224364738,-0.25184674038281973) circle (1.5pt);
\draw[color=qqqqff] (8.314255658461247,-0.0706427597205999) node {$C$};
\draw [fill=qqqqff] (4.470142640127001,0.6800594458800253) circle (1.5pt);
\draw[color=qqqqff] (4.6772329037409675,0.6800594458800253) node {$O$};
\draw [fill=uuuuuu] (2.2966858616022594,1.8384717658325291) circle (1.5pt);
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\draw[color=uuuuuu] (6.178637314942222,2.3756109792193683) node {$D$};
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\draw[color=uuuuuu] (4.405426932747637,-0.40716443809329395) node {$E$};
\end{scriptsize}
\end{tikzpicture}



*** Error message:
Error: Nothing to show, formula is empty