Category: Limits

Question Number 155639 by cortano last updated on 03/Oct/21 Commented by yeti123 last updated on 03/Oct/21 $$\underset{\theta \to 0}{\lim }\frac{\sin 2\theta }{1-\cos \theta }=\underset{\theta \to 0}{\lim }\frac{\sin 2\theta }{{2\sin }^2\left(\theta /2\right)}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2}\theta}{\mathrm{2}\theta}×\frac{\left(\theta/\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{2sin}^{\mathrm{2}} \left(\theta/\mathrm{2}\right)}×\frac{\mathrm{2}\theta}{\left(\theta/\mathrm{2}\right)^{\mathrm{2}}…

Question Number 90077 by manuel__ last updated on 21/Apr/20 $${lim}_{x\to \mathrm{\infty }}(\sin (x+\frac{1}{x})-sin\left(x\right))=?$$ Commented by jagoll last updated on 21/Apr/20 $$\sin (\mathrm{x}+\frac{1}{\mathrm{x}})-\sin \left(\mathrm{x}\right)=$$$$2\cos \left(\frac{2\mathrm{x}+\frac{1}{\mathrm{x}}}{2}\right)\sin \left(\frac{1}{2\mathrm{x}}\right)=$$$$\mathrm{2cos}\:\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2x}}\right)\:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{2x}}\right)…

Question Number 24405 by chernoaguero@gmail.com last updated on 17/Nov/17 $$\mathrm{Find}\mathrm{the}\mathrm{horizontal}\mathrm{assymptot}$$$$\underset{x\to \mathrm{\infty }}{\lim }\frac{\sqrt[6]{{3\mathrm{x}}^2+4}}{\sqrt[9]{1-{2\mathrm{x}}^3}}$$$$$$ Terms of Service Privacy Policy Contact:…

Question Number 89922 by student work last updated on 20/Apr/20 Commented by john santu last updated on 20/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\mathrm{5}−\mathrm{2}{x}^{\mathrm{2}} }\:\leqslant\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:\leqslant\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt{\mathrm{5}+\mathrm{2}{x}^{\mathrm{2}} } \…

Question Number 155392 by cortano last updated on 30/Sep/21 $$\underset{x\to 0}{\lim }{\left(\frac{{(a^{x+1}+b^{x+1})}^2}{a+b}\right)}^{\frac{1}{x}}=\dots ?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com