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 $|q|<1$)

điền giới từ thích hợp bằng in, on, at 
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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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