Question Number 222889 by Tawa11 last updated on 10/Jul/25 Commented by mr W last updated on 10/Jul/25 $${such}\:{a}\:{bench}: \\ $$ Commented by mr W last…
Question Number 222922 by MrGaster last updated on 10/Jul/25 $$ \\ $$$$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} {J}_{\mathrm{0}} \left(\mathrm{ln}\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$ Answered by MrGaster last updated on 11/Jul/25 $${u}=\mathrm{ln}\frac{\mathrm{1}}{{x}}\Rightarrow{x}={e}^{−{u}}…
Question Number 222885 by gabthemathguy25 last updated on 10/Jul/25 Answered by MrGaster last updated on 10/Jul/25 Commented by gabthemathguy25 last updated on 10/Jul/25 nice Answered…
Question Number 222881 by MrGaster last updated on 10/Jul/25 $$ \\ $$$$\:\int_{\mathrm{0}} ^{\infty} {t}^{{a}} {e}^{−{t}} \mathrm{erf}\left({kt}\right){dt},{a}>\mathrm{0},{k}>\mathrm{0} \\ $$ Answered by gabthemathguy25 last updated on 10/Jul/25…
Question Number 222845 by Nicholas666 last updated on 09/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Evaluate}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:\left(−\mathrm{1}\right)^{{k}} \:\begin{pmatrix}{\mathrm{2}{n}\:−\:{k}}\\{\:\:\:\:\:\:\:\:{k}}\end{pmatrix} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 222847 by OmoloyeMichael last updated on 09/Jul/25 $$\boldsymbol{{let}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{1}.\mathrm{013}\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{5}.\mathrm{262}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{0}.\mathrm{01732}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{0}.\mathrm{8389}\boldsymbol{{x}} \\ $$$$−\mathrm{1}.\mathrm{912}.\:\boldsymbol{{Evaluate}}\:\boldsymbol{{f}}\left(\mathrm{2}.\mathrm{279}\right)\:\boldsymbol{{by}}\:\boldsymbol{{first}}\:\boldsymbol{{calculating}} \\ $$$$\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{2}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{3}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{4}} \boldsymbol{{and}}\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{5}} \:\boldsymbol{{using}} \\ $$$$\boldsymbol{{four}}−\boldsymbol{{digit}}\:\boldsymbol{{round}}\:\boldsymbol{{arithmetic}}.\:\boldsymbol{{hence}},\boldsymbol{{compute}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{absolute}}\:\boldsymbol{{and}}\:\boldsymbol{{relative}}\:\boldsymbol{{errors}}.…
Question Number 222838 by MrGaster last updated on 09/Jul/25 $$\:\:\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}=−\frac{\pi^{\mathrm{2}} }{\mathrm{20}} \\ $$ Answered by MrGaster last updated on 09/Jul/25 $$ \\…
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Question Number 222856 by OmoloyeMichael last updated on 09/Jul/25 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{possible}}\:\boldsymbol{{root}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{6}=\mathrm{0} \\ $$$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{fixed}}\:\boldsymbol{{point}}\:\boldsymbol{{iteration}}\:\boldsymbol{{method}}? \\ $$ Answered by AntonCWX8 last updated on 09/Jul/25 $${x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…