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Question-216953

Question Number 216953 by mustaphapelumi last updated on 25/Feb/25 Commented by Ghisom last updated on 26/Feb/25 $$\mathrm{or}\:\mathrm{use}\:\mathrm{l}'\mathrm{H}\hat {\mathrm{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{{d}\left[\mathrm{sin}\:{x}\right]}{{dx}}}{\frac{{d}\left[{x}\right]}{{dx}}}\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}}\:=\mathrm{1} \\ $$…

Question-216925

Question Number 216925 by Engr_Jidda last updated on 24/Feb/25 Answered by mehdee7396 last updated on 24/Feb/25 $${s}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}+\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}+…+\int_{\mathrm{0}} ^{\mathrm{10}} \left(\mathrm{4}{u}+\mathrm{1}\right){du} \\ $$$$\left.=\left.\left(\left.\mathrm{2}{u}^{\mathrm{2}}…