Category: Limits

Question Number 216055 by efronzo1 last updated on 26/Jan/25 $$\underset{x\to 0}{\lim }\frac{\sin {}^{2}2\mathrm{x}}{\sqrt[3]{\cos \mathrm{x}}-\sqrt[4]{\cos \mathrm{x}}}=?$$ Answered by golsendro last updated on 27/Jan/25 $$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{x}}}…

Question Number 216014 by mathlove last updated on 25/Jan/25 $$\underset{\mathrm{\Delta }x\to cos\frac{\pi }{2}}{\lim }\frac{{\sin }^3(\mathrm{\Delta }x+x)-{sin}^{3}x}{2^{-1}\cdot \mathrm{\Delta }x}=?$$ Answered by MrGaster last updated on 26/Jan/25 $$=\mathrm{2}\centerdot\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}^{\mathrm{3}}…

Question Number 215831 by golsendro last updated on 19/Jan/25 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\sqrt{{(\mathrm{x}+1)}^3}-\sqrt{{(\mathrm{x}-1)}^3}}{\sqrt{\mathrm{x}}}=?$$ 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 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 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}} } \…