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Question-203374

Question Number 203374 by otchereabdullai@gmail.com last updated on 17/Jan/24 Answered by Calculusboy last updated on 18/Jan/24 $$\boldsymbol{{Solution}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}\:\:\:\left(\boldsymbol{{by}}\:\boldsymbol{{using}}\:\boldsymbol{{algebraic}}\:\boldsymbol{{methods}}\right) \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}}=\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}} \\ $$$$\boldsymbol{{NB}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tanax}}}{\boldsymbol{{x}}}=\mathrm{1}\:\:\boldsymbol{{then}}\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}}…

sin6-sin12-sin24-sin28-

Question Number 203242 by sulaymonnorboyev140 last updated on 13/Jan/24 $${sin}\mathrm{6}°\centerdot{sin}\mathrm{12}°\centerdot{sin}\mathrm{24}°\centerdot{sin}\mathrm{28}° \\ $$ Answered by MathematicalUser2357 last updated on 15/Jan/24 $$\mathrm{4}.\mathrm{1498}×\mathrm{10}^{−\mathrm{3}} \\ $$ Terms of Service…

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Question Number 203270 by MrGHK last updated on 13/Jan/24 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\mathrm{4}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2024}^{\mathrm{2023}} \\ $$ Answered by Frix last updated on 14/Jan/24 $$\mathrm{Last}\:\mathrm{4}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{2024}^{{n}} \\ $$$${n}=\mathrm{1}\:\mathrm{2024} \\ $$$$\mathrm{Then}\:\mathrm{a}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{length}\:\mathrm{50} \\…

Let-s-define-linear-Operator-L-as-L-0-e-st-L-W-t-W-t-is-inverse-function-of-y-t-te-t-t-1-e-

Question Number 203199 by MathedUp last updated on 12/Jan/24 $$\mathrm{Let}'{s}\:\mathrm{define}\:\mathrm{linear}\:\mathrm{Operator}\:\boldsymbol{\mathcal{L}}\:\mathrm{as}\:\boldsymbol{\mathcal{L}}=\int_{\mathrm{0}} ^{\infty} \:{e}^{−{st}} \centerdot \\ $$$$\boldsymbol{\mathcal{L}}\left\{{W}\left({t}\right)\right\}=??? \\ $$$${W}\left({t}\right)\:\mathrm{is}\:\mathrm{inverse}\:\mathrm{function}\:\mathrm{of}\:{y}\left({t}\right)={te}^{{t}} \:,\:{t}\in\left[−\frac{\mathrm{1}}{{e}},\infty\right) \\ $$ Commented by shunmisaki007 last updated…

find-the-last-four-digits-of-2022-2023-2023-2022-

Question Number 203192 by MrGHK last updated on 12/Jan/24 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2022}^{\mathrm{2023}} +\mathrm{2023}^{\mathrm{2022}} \\ $$ Answered by AST last updated on 12/Jan/24 $${x}=\mathrm{2022}^{\mathrm{2023}} +\mathrm{2023}^{\mathrm{2022}} \overset{\mathrm{16}} {\equiv}\mathrm{6}^{\mathrm{2023}} +\mathrm{7}^{\mathrm{2022}}…