Chapter Limit : All Importants Formula
Formula Summary
1. \lim_{x\rightarrow 0}\frac {e^x-1}{x}=1
2. \lim_{x\rightarrow 0}\frac {a^x-1}{x}=\small log_{e}a
3. \lim_{x\rightarrow 0}\frac {log_{e}(1+x)}{x}=\small 1
4. \lim_{x\rightarrow 0}(1+x)^{\frac{1}{x}}=\small e
5. \lim_{x\rightarrow 0}(1+ax)^{\frac{1}{x}}=\small e^a
6. \lim_{x\rightarrow \infty}(1+\frac{1}{x})^x=\small e
7. \lim_{x\rightarrow \infty}(1+\frac{1}{f(x)})^{f(x)}=\small e
8. \lim_{x\rightarrow \infty}(1+\frac{a}{x})^x=\small e^a
9. \lim_{x\rightarrow 0}(1+\frac{1}{f(x)})^{f(x)}=\small e
10. \lim_{x\rightarrow a}[f(x)]^{g(x)}=\small e^{\lim_{x\rightarrow a}[f(x)-1]g(x)}