Category: Limits

Question Number 175217 by mnjuly1970 last updated on 23/Aug/22 $$$$$${lim}_{x\to 0}\{\lfloor \frac{cos\left(x\right)}{x}\rfloor -\lfloor \frac{1+cos\left(x\right)}{1-cos\left(x\right)}\rfloor \}$$ Commented by kaivan.ahmadi last updated on 24/Aug/22 $${we}\:{know}\:{that}\:\left[{x}\right]_{{x}\rightarrow\infty} \sim{x}\:{so} \…

Question Number 44085 by rk last updated on 21/Sep/18 $$lim\mathrm{x}\to 0\left[\frac{\sin \mid x\mid }{x}\right]$$ Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on…

Question Number 175137 by cortano1 last updated on 20/Aug/22 $$\underset{x\to 2}{\lim }\frac{\sqrt[5]{5x-9}\sqrt[4]{4x-7}\sqrt[3]{3x-5}\sqrt{2x-3}-1}{x-2}=?$$ Answered by Ar Brandon last updated on 20/Aug/22 $$\mathcal{L}=\underset{x\to 2}{\lim }\frac{\sqrt[5]{5x-9}\sqrt[4]{4x-7}\sqrt[3]{3x-5}\sqrt{2x-3}-1}{x-2}$$$$\:\:\:\:\:=\underset{{t}\rightarrow\mathrm{0}}…

Question Number 109462 by 150505R last updated on 23/Aug/20 Answered by mathmax by abdo last updated on 24/Aug/20 $$\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} }\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\left[\mathrm{k}^{\mathrm{2}} \mathrm{x}\:+\mathrm{k}^{\mathrm{2}} \right]\:\Rightarrow\:\mathrm{A}_{\mathrm{n}}…

Question Number 174915 by cortano1 last updated on 14/Aug/22 $$Findthevalueofaforwhich$$$$thelimit\underset{x\to 0}{\lim }\frac{\sin \left(ax\right)-\arctan x-x}{x^3+x^4}$$$$isfiniteandthenevaluatethelimit$$ Answered by Ar Brandon last updated…