Question Number 83205 by Rio Michael last updated on 28/Feb/20 $$\int_{\mathrm{0}} ^{{ln}\mathrm{2}} \frac{\mathrm{1}}{{cosh}\left({x}\:+\:{ln}\mathrm{4}\right)}{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 28/Feb/20 $${I}\:=_{{x}+{ln}\mathrm{4}={t}}…
Question Number 83202 by Rio Michael last updated on 28/Feb/20 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{4}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{maclaurin}\left[\right. \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{3}{x}\right)\:\mathrm{hence}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{if}\:{x}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{higher}\:\mathrm{powers}\:\mathrm{of}\:{x}\:\mathrm{are}\:\mathrm{negleted}, \\ $$$$\mathrm{then}\: \\ $$$$\:\:\:\left(\mathrm{1}\:+\:\mathrm{3}{x}\right)^{\frac{\mathrm{3}}{{x}}} \:=\:{e}^{\mathrm{6}} \left(\mathrm{1}\:−\mathrm{9}{x}\right) \\ $$ Commented…
Question Number 148739 by Tawa11 last updated on 30/Jul/21 Commented by Tawa11 last updated on 30/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\:\:\:\:\:\:\mathrm{JSMT} \\ $$ Commented by Tawa11 last updated on…
Question Number 148733 by Rustambek last updated on 30/Jul/21 $${tg}\left(\alpha\right)+{tg}\left(\beta\right)=\mathrm{4} \\ $$$${cos}\left(\alpha\right)+{cos}\left(\beta\right)=\frac{\mathrm{1}}{\mathrm{5}} \\ $$$${tg}\left(\alpha+\beta\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148732 by ethiork last updated on 30/Jul/21 $$\:\:\:\:\:\:{show}\:{that}\: \\ $$$$\mathrm{8}^{{n}} \:−\mathrm{3}^{{n}} \:{is}\:{divisible}\:{by}\:\mathrm{5}\:\:{for}\:{all}\:{natural} \\ $$$${number}. \\ $$ Answered by Rasheed.Sindhi last updated on 30/Jul/21…
Question Number 148724 by Sozan last updated on 30/Jul/21 $${find}\:{laurent}\:{series}\:{f}\left({z}\right)=\frac{\mathrm{1}}{{z}^{\mathrm{2}} −{z}+\mathrm{1}}\:\:,\mathrm{0}<\mid{z}−\mathrm{1}\mid<\mathrm{1} \\ $$ Answered by mathmax by abdo last updated on 30/Jul/21 $$\mathrm{the}\:\mathrm{way}\:\mathrm{of}\:\mathrm{this}\:\mathrm{kind}\:\mathrm{is}\:\mathrm{to}\:\mathrm{use}\:\mathrm{changement}\:\mathrm{z}−\mathrm{1}=\mathrm{y}\:\Rightarrow \\ $$$$\mathrm{f}\left(\mathrm{z}\right)=\varphi\left(\mathrm{y}\right)=\frac{\mathrm{1}}{\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 83188 by john santu last updated on 28/Feb/20 $$\mathrm{If}\:\underset{\mathrm{a}\:=\:\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left(\mathrm{2a}+\mathrm{1}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{n}^{\mathrm{2}} +\mathrm{4n}−\mathrm{5}\right)\mathrm{x}+\mathrm{16} \\ $$$$=\:\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{n}\:\in\:\mathbb{Z}^{+} \:.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{x}\:+\mathrm{n}\:?\: \\ $$ Answered…
Question Number 17653 by 1kanika# last updated on 09/Jul/17 $$\mathrm{A}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{with}\:\mathrm{its}\:\mathrm{end}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{coordinate} \\ $$$$\mathrm{axes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{its}\:\mathrm{intersect}\:\mathrm{on}\:\mathrm{the}\:\mathrm{coordinate}\: \\ $$$$\mathrm{axes}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{C}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{this}\:\mathrm{segment}\:. \\ $$$$\mathrm{Ans}.\:\mathrm{is}\:\:\:\mathrm{8}\left(\mid\mathrm{x}\mid^{\mathrm{3}} +\mid\mathrm{y}\mid^{\mathrm{3}}…
Question Number 83189 by john santu last updated on 28/Feb/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{3}\:^{\mathrm{rd}} \:\mathrm{derivative}\:\mathrm{of}\: \\ $$$$\mathrm{x}^{\mathrm{5}} \:\mathrm{ln}\left(\mathrm{2x}\right)\:\mathrm{using}\:\mathrm{the}\:\mathrm{Leibniz}\:\mathrm{theorem} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$\mathrm{y}\:=\:\mathrm{x}^{\mathrm{5}}…
Question Number 148720 by qaz last updated on 30/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{Talor}\:\mathrm{series}\:\mathrm{of}\:\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{at}\:\mathrm{x}=\mathrm{0}. \\ $$ Answered by mathmax by abdo last updated on 30/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\:\:\mathrm{we}\:\mathrm{have}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty}…