Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 187164 by mathlove last updated on 14/Feb/23

Answered by qaz last updated on 14/Feb/23

$$\underset{p\to ln\frac{1}{2}}{lim}\frac{ln2+ln2cosp}{{\left(cosln\frac{1}{\sqrt{2}}\right)}^2}=\frac{(1+cosln2)ln2}{cos{}^2\frac{1}{2}ln2}=\frac{\left[2\cos {}^2\frac{1}{2}ln2\right]ln2}{{cos}^2\frac{1}{2}ln2}=2ln2$$$$\underset{p=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^p}{p+1}=\underset{p=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{p-1}}{p}=ln2$$$$\frac{d}{dx}\left(\frac{x}{{\left(\sin x\right)}^2+{\left(\cos x\right)}^2}\right)=\frac{dx}{dx}=1$$$$\underset{t\to \mathrm{\infty }}{lim}(2t+1)\frac{(t+2)!+(t+1)!}{t+3}\left(\frac{3^t-2^t}{2^t+5}\right)$$$$=\underset{t\to \mathrm{\infty }}{lim}(2t+1)(t+1)!\cdot \frac{1-{\left(\frac{2}{3}\right)}^t}{{\left(\frac{2}{3}\right)}^t+\frac{5}{3^t}}=+\mathrm{\infty }$$$$I={\int }_{ln2}^{2ln2}(+\mathrm{\infty })dx=?$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com