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Category: Differentiation

Find-the-area-bounded-by-the-curve-y-3x-2-2x-3-the-x-axis-and-the-line-x-5-and-x-2-

Question Number 32775 by NECx last updated on 02/Apr/18 $${Find}\:{the}\:{area}\:{bounded}\:{by}\:{the} \\ $$$${curve}\:{y}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3},{the}\:{x}\:{axis} \\ $$$${and}\:{the}\:{line}\:{x}=\mathrm{5}\:{and}\:{x}=\mathrm{2} \\ $$ Answered by MJS last updated on 02/Apr/18 $$\mathrm{1}.\:\mathrm{check}\:\mathrm{the}\:\mathrm{zeros}…

Question-98213

Question Number 98213 by me2love2math last updated on 12/Jun/20 Commented by bemath last updated on 12/Jun/20 $$\mathrm{let}\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{t}\:,\:\mathrm{t}\:\rightarrow\mathrm{0}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{3}{t}\right)}{{t}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3t}}}{\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{3} \\ $$ Answered by…

If-sin-x-ln-2-x-x-then-find-Im-m-n-

Question Number 163732 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$ Terms of…

K-x-3-cos-x-5-4sin-x-max-K-x-min-K-x-

Question Number 163700 by blackmamba last updated on 09/Jan/22 $$\:\:\mathcal{K}\left({x}\right)\:=\:\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4sin}\:{x}} \\ $$$$\:\left.\begin{matrix}{{max}\:\mathcal{K}\left({x}\right)}\\{{min}\:\mathcal{K}\left({x}\right)}\end{matrix}\right\}\:=? \\ $$ Answered by mr W last updated on 10/Jan/22 $$\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4}\:\mathrm{sin}\:{x}}={k} \\ $$$$\mathrm{3}\:\mathrm{cos}\:{x}−\mathrm{4}{k}\:\mathrm{sin}\:{x}=\mathrm{5}{k}…

0-1-Li-2-x-2-dx-m-n-

Question Number 163682 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{Li}_{\:\mathrm{2}} ^{\:} \left({x}\:\right)\right)^{\:\mathrm{2}} {dx}\:=\:?\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\: \\ $$$$\:\:\:\:\:−−−\:−−− \\ $$$$\:\:\:\: \\ $$ Answered by…