Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 161361 by cortano last updated on 17/Dec/21

  lim_(x→0)  (((√(x+1)) +((1+2x))^(1/h) −2)/x) = (3/5)     h^3 −(2/9)(h+7)=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}\:+\sqrt[{{h}}]{\mathrm{1}+\mathrm{2}{x}}−\mathrm{2}}{{x}}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\: \\ $$$$\:\:{h}^{\mathrm{3}} −\frac{\mathrm{2}}{\mathrm{9}}\left({h}+\mathrm{7}\right)=? \\ $$

Commented by vietanhdz last updated on 17/Dec/21

(√(x+1))−1∼(x/2) if x∼0  (1+2x)^(1/h) −1∼((2x)/h) if x∼0  suy ra (1/2)+(2/h)=(3/5) h=20

$$\sqrt{{x}+\mathrm{1}}−\mathrm{1}\sim\frac{{x}}{\mathrm{2}}\:{if}\:{x}\sim\mathrm{0} \\ $$$$\left(\mathrm{1}+\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{{h}}} −\mathrm{1}\sim\frac{\mathrm{2}{x}}{{h}}\:{if}\:{x}\sim\mathrm{0} \\ $$$${suy}\:{ra}\:\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{{h}}=\frac{\mathrm{3}}{\mathrm{5}}\:{h}=\mathrm{20} \\ $$$$ \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com