Zacharias/Analys-och-Linj-r-algibra
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@@ -24,8 +24,7 @@
- $\left[\infty^0\right]$ form **Ex**: $$\lim_{x\to\infty}x^{1/x}$$
- $\left[1^\infty\right]$ form: **Ex**: $$\lim_{x\to0}(1+x)^{1/x}$$
- $\left[\infty-\infty\right]$ form: $$\lim_{x\to\infty}\left(\sqrt{x^2+5x+1}-\sqrt{x^2+3x-5}\right)$$
- **Ex**: $$
\begin{align}
- **Ex**: $$ \begin{align}
\lim_{x\to\infty}\left(\sqrt{x^2+5x+1}-\sqrt{x^2+3x-5}\right)\\
=\lim_{x\to\infty}\frac{\left(\sqrt{x^2+5x+1}-\sqrt{x^2+3x-5}\right)\left(\sqrt{x^2+5x+1}+\sqrt{x^2+3x-5}\right)}{\sqrt{x^2+5x+1}+\sqrt{x^2+3x-5}}\\
=\lim_{x\to\infty}\frac{\left(\cancel{x^2}+5x+1\right)-\left(\cancel{x^2}+3x-5\right)}{\sqrt{x^2+5x+1}+\sqrt{x^2+3x-5}}\\