Question Number 166584 by amin96 last updated on 22/Feb/22 Commented by bobhans last updated on 22/Feb/22 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{a}\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \Rightarrow\mathrm{12}=\mathrm{a}\left(\mathrm{4}\right);\:\mathrm{a}=\mathrm{3} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \Rightarrow\mathrm{f}\left(\mathrm{10}\right)=\mathrm{3}×\mathrm{64}=\mathrm{192} \\ $$ Answered by…
Question Number 166572 by qaz last updated on 22/Feb/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{2n}} {\sum}}\mathrm{2}^{−\mathrm{k}} \mathrm{cos}\:\sqrt{\frac{\mathrm{k}}{\mathrm{n}}}=? \\ $$ Answered by alephzero last updated on 23/Feb/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{0}}…
Question Number 166560 by mathlove last updated on 22/Feb/22 Answered by qaz last updated on 22/Feb/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{ln}\left(\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} +\mathrm{x}^{\mathrm{3}} \right)−\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\mathrm{x}\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }} \\ $$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{ln}\frac{\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} +\mathrm{x}^{\mathrm{3}}…
Question Number 166522 by mnjuly1970 last updated on 21/Feb/22 Commented by CAIMAN last updated on 21/Feb/22 1 Answered by MJS_new last updated on 21/Feb/22 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 100920 by ajfour last updated on 29/Jun/20 $${Find}\:{limit} \\ $$$$\:\:\:\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\right)\:\:\:{and} \\ $$$$\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\right)\:\:. \\ $$ Commented by bramlex last updated…
Question Number 166212 by mnjuly1970 last updated on 15/Feb/22 $$ \\ $$$$\:\:\:{x},\:{y}\:,\:{z}\:\in\mathbb{R}^{\:+} \:{and}\:\:{x}\geqslant{y}\geqslant{z} \\ $$$$\:\:\:\:{and}\:\: \\ $$$$\:\:\:\:{x}^{\mathrm{2}} +{y}^{\:\mathrm{2}} +{z}^{\:\mathrm{2}} \geqslant\:\mathrm{2}{xy}\:+\mathrm{2}{xz}+\mathrm{2}{yz} \\ $$$$\:\:\:\:\:\:\mathrm{F}{ind}\:\:\:\:\:\mathrm{M}{in}\left(\frac{{x}}{{z}}\:\right)=? \\ $$ Answered…
Question Number 35021 by rahul 19 last updated on 14/May/18 $${Find}\:{the}\:{points}\:{at}\:{which}\:{the}\:{given} \\ $$$${function}\:{is}\:{discontinuous}\:: \\ $$$${f}\left({x}\right)=\:\mid{x}\mid\:{sgn}\:\left({x}^{\mathrm{3}} −{x}\right)\:. \\ $$ Commented by ajfour last updated on 14/May/18…
Question Number 35023 by ajfour last updated on 14/May/18 Commented by ajfour last updated on 14/May/18 $${Answer}\:{to}\:{Q}.\mathrm{35021} \\ $$ Answered by rahul 19 last updated…
Question Number 34982 by rahul 19 last updated on 14/May/18 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{nx}^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right){x}^{{n}} +\mathrm{1}}{\left({e}^{{x}} −{e}\right)\mathrm{sin}\:\pi{x}}\:=\:? \\ $$ Commented by math khazana by abdo last updated…
Question Number 34951 by rahul 19 last updated on 13/May/18 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{e}×{a}}{{n}}\right)^{{n}} \:=\:?\: \\ $$$${Here}\:{a}\epsilon\:\mathbb{R}^{+} \\ $$ Answered by MJS last updated on 14/May/18 $${a}\mathrm{e}={p}\in\mathbb{R}^{+}…