极限的计算

极限的计算

\(\lim\limits_{x \to 2}\frac{x^3+5}{x^2-1}=\frac{8+5}{3}=\frac{13}{3}\)

\(\lim\limits_{x \to 1}\frac{x^2+2x+3}{2x^2+3x-1}\) \(答案：\frac{3}{2}\)

\(\lim\limits_{x \to 0^+}\frac{2^x}{3+\ln(1+x)}\) \(答案：\frac{1}{3}\)

极限计算：代入

\(\lim\limits_{x\to 0}\frac{1}{x}\) \(\infty\)

\(\frac{1}{0.1}=10\)

重视

\(\frac{1}{0}=\infty\)
\(\frac{1}{\infty}=0\)
\(\frac{0}{\infty}=0\)
\(\frac{\infty}{0}=\infty\)

例：\(\lim\limits_{n\to \infty}\sqrt[n]4\)
\(\sqrt[a]b=x\frac{b}{a}\)