Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 1468 by havandip last updated on 11/Aug/15

Answered by 123456 last updated on 11/Aug/15

$$\underset{x\to -\mathrm{\infty }}{\lim }f\left(x\right)=\mathrm{L}$$$$\mathrm{\forall }ϵ>0,\mathrm{\exists }\mathrm{M}\in \mathbb{R},\mathrm{\forall }x<\mathrm{M},\mid f\left(x\right)-\mathrm{L}\mid <ϵ$$

Commented by 123456 last updated on 11/Aug/15

$$\underset{x\to 0}{\lim }\frac{a^x-1}{x}=\ln a$$

Commented by 123456 last updated on 11/Aug/15

$$a>1$$$$x<\mathrm{M}<0\Rightarrow \frac{1}{\mathrm{M}}<\frac{1}{x}<0$$$$a^x<a^{\mathrm{M}}\Rightarrow a^x-1<a^{\mathrm{M}}-1$$$$\frac{a^x-1}{x}>\frac{a^{\mathrm{M}}-1}{x}>\frac{a^{\mathrm{M}}-1}{\mathrm{M}}$$$$\frac{a^x-1}{x}>\frac{a^x-1}{\mathrm{M}}>\frac{a^{\mathrm{M}}-1}{\mathrm{M}}$$$$0<\frac{a^x-1}{x}<\frac{a^{\mathrm{M}}-1}{\mathrm{M}}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com