Question Number 136693 by liberty last updated on 25/Mar/21 Commented by Olaf last updated on 25/Mar/21 $${f}\left({x}\right)\:=\:{mx}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +{kx}−\mathrm{18} \\ $$$$=\:\left(\mathrm{6}−{x}−{x}^{\mathrm{2}} \right)\left(−{mx}−\mathrm{3}\right) \\ $$$$=\left({x}^{\mathrm{2}} +{x}−\mathrm{6}\right)\left({mx}+\mathrm{3}\right)…
Question Number 71143 by mathmax by abdo last updated on 12/Oct/19 $${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{calculate}\:{A}_{{n}} \:{interms}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Commented by mathmax by…
Question Number 136598 by I want to learn more last updated on 23/Mar/21 Answered by Olaf last updated on 23/Mar/21 $${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} −{x}−\mathrm{2} \\ $$$${f}\left(−\mathrm{2}\right)\:=\:\mathrm{4} \\…
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Question Number 70891 by Henri Boucatchou last updated on 09/Oct/19 $$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{x}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)….\left(\boldsymbol{{x}}−\mathrm{10}\right) \\ $$$$\boldsymbol{{f}}\:'\left(\mathrm{0}\right)\:=\:? \\ $$ Commented by kaivan.ahmadi last updated on 09/Oct/19 $${let}\:{g}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−\mathrm{10}\right)\Rightarrow{f}\left({x}\right)={xg}\left({x}\right) \\ $$$$\Rightarrow{f}'\left({x}\right)={g}\left({x}\right)+{xg}'\left({x}\right)\Rightarrow…
Question Number 136404 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{n}\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{n}+\mathrm{3}\right)} \\ $$ Answered by mindispower last updated on 21/Mar/21…
Question Number 136370 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{letf}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{arctan}\left(\frac{\pi}{\mathrm{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integer}\:\mathrm{serie} \\ $$ Answered by…
Question Number 5236 by sanusihammed last updated on 02/May/16 $${find}\:{the}\:{range}\:{and}\:{domain}\:{of}\: \\ $$$$\left({i}\right)\:\:{y}\:=\:\mid−{x}\mid \\ $$$$\left({ii}\right)\:{y}\:=\:\mid{x}−\mathrm{5}\mid \\ $$ Answered by FilupSmith last updated on 02/May/16 $$\left({i}\right) \\…
Question Number 5237 by sanusihammed last updated on 02/May/16 $${find}\:{the}\:{domain}\:{and}\:{range}\:{of}\: \\ $$$${y}\:=\:\left[_{\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:<\mathrm{2}} ^{\:\mathrm{3}{x}−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:\geqslant\:\mathrm{2}} \right. \\ $$ Answered by FilupSmith last updated on 02/May/16 $${Domain}\:=\:\left\{{x}:\:−\infty\leqslant{x}\leqslant\infty\right\}…
Question Number 5235 by sanusihammed last updated on 02/May/16 $${Find}\:{the}\:{range}\:{and}\:{domain}\:{of}\: \\ $$$${y}\:=\:\frac{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{10}\right)}{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}} \\ $$ Answered by Yozzii last updated on 02/May/16 $${x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}=\left({x}+\mathrm{3}\right)^{\mathrm{2}}…