Gieo con xúc sắc hai lần, $n\left(\Omega \right)=6.6=36$.

Gọi $A$ là biến cố: “Tổng số chấm xuất hiện trong hai lần gieo bằng $8$”

Khi đó $A=\left\{\left(2;6\right),\left(3;5\right),\left(4;4\right),\left(5;3\right),\left(6;2\right)\right\}$ $\Rightarrow n\left(A\right)=5$

Xác suất $P\left(A\right)=\frac{5}{36}$.

Lời giải:
\(\lim\limits_{x\to +\infty}\frac{3^x-4.2^{x+1}-3}{3.2^x+4^x}=\lim\limits_{x\to +\infty}\frac{(\frac{3}{4})^x-\frac{8}{2^{x}}-\frac{3}{4^x}}{3.\frac{1}{2^x}+1}=\frac{0-0-0}{0+1}=0\) (nhớ rằng $\lim q^n=0$ khi $|q|<1$)

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\(\lim\limits_{x\rightarrow-2}=\dfrac{x-1+\sqrt{2x^2+1}}{4-x^2}\)

\(=\lim\limits_{x\rightarrow-2}=\dfrac{\left[\left(x-1\right)+\sqrt{2x^2+1}\right]\left[\left(x-1\right)-\sqrt{2x^2+1}\right]}{\left(4-x^2\right)\left[\left(x-1\right)-\sqrt{2x^2+1}\right]}\)

\(=\lim\limits_{x\rightarrow-2}\dfrac{\left(x-1\right)^2-\left(2x^2+1\right)}{\left(4-x^2\right)\left[\left(x-1\right)-\sqrt{2x^2+1}\right]}\)

\(=\lim\limits_{x\rightarrow-2}\dfrac{x^2-2x+1-2x^2-1}{\left(4-x^2\right)\left[\left(x-1\right)-\sqrt{2x^2+1}\right]}\)

\(=\lim\limits_{x\rightarrow-2}\dfrac{-x^2-2x}{\left(4-x^2\right)\left[\left(x-1\right)-\sqrt{2x^2+1}\right]}\)

\(=\lim\limits_{x\rightarrow-2}=-\dfrac{x}{\left(2-x\right)\left(x-1-\sqrt{2x^2+1}\right)}\)

\(=-\dfrac{1}{12}\)

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