Question Number 215884 by golsendro last updated on 20/Jan/25 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{6x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{5x}}\:=? \\ $$$$\:\:\:\: \\ $$ Answered by oubiji last updated on 20/Jan/25 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{6x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{5x}}\: \\…
Question Number 215831 by golsendro last updated on 19/Jan/25 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} }−\sqrt{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{3}} }}{\:\sqrt{\mathrm{x}}}\:=? \\ $$ Answered by efronzo1 last updated on 19/Jan/25 $$\:\:\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{6x}^{\mathrm{2}} +\mathrm{2}}{\:\sqrt{\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}}…
Question Number 215808 by efronzo1 last updated on 19/Jan/25 $$\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by golsendro last updated on 19/Jan/25 $$\:\:=\:\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} −\mathrm{3}}{{x}}\right)} \\…
Question Number 215779 by ucup last updated on 18/Jan/25 Commented by MathematicalUser2357 last updated on 18/Jan/25 The "Sehingga" looks like "Sh-nigga", so I flagged your post as inappropriate. Commented by AntonCWX last updated on 18/Jan/25 $${Sehingga}\:{means}\:{until}\:{in}\:{English}.…
Question Number 215748 by MrGaster last updated on 17/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\underset{{k}=\mathrm{1}} {\overset{{n}+\mathrm{1}} {\prod}}\Gamma\left(\frac{\mathrm{1}}{{k}}\right)\right]^{\frac{\mathrm{1}}{{n}+\mathrm{1}}} −\left[\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\Gamma\left(\frac{\mathrm{1}}{{k}}\right)\right]^{\frac{\mathrm{1}}{{n}}} \\ $$ Answered by MrGaster last updated on 02/Feb/25…
Question Number 215739 by universe last updated on 16/Jan/25 Answered by MrGaster last updated on 19/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}+\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}{n}^{{k}} }{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{n}} } \\…
Question Number 215718 by mathlove last updated on 16/Jan/25 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({ln}\frac{\mathrm{9}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}{x}} =? \\ $$$$ \\ $$ Answered by mehdee7396 last updated on 17/Jan/25 $${if}\:\:{x}\rightarrow+\infty\Rightarrow{lim}\left({ln}\frac{\mathrm{9}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}{x}} =+\infty…
Question Number 215667 by mathlove last updated on 14/Jan/25 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{sec}\left(\frac{\pi}{\mathrm{2}}{x}\right)\left({arctanx}−\frac{\pi}{\mathrm{4}}\right)=? \\ $$ Answered by issac last updated on 14/Jan/25 $$\mathrm{sec}\left(\frac{\pi}{\mathrm{2}}\right)\left(\mathrm{arctan}\left(\mathrm{1}\right)−\frac{\pi}{\mathrm{4}}\right) \\ $$ Commented by…
Question Number 215343 by RoseAli last updated on 03/Jan/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{3}{x}\mathrm{cos5}{x}\:}{{x}^{\mathrm{2}} } \\ $$ Commented by Frix last updated on 04/Jan/25 $$\mathrm{Does}\:\mathrm{not}\:\mathrm{exist}. \\ $$ Answered…
Question Number 215051 by MrGaster last updated on 27/Dec/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} +\mathrm{1}}{\:\sqrt{{k}^{\mathrm{2}} +\mathrm{4}}}=? \\ $$$$ \\ $$ Answered by MathematicalUser2357 last…