Question Number 32297 by abdo imad last updated on 22/Mar/18 $${calculate}\:\sum_{{n}\geqslant\mathrm{0}} \:\frac{{n}+\mathrm{2}^{{n}} }{{n}!}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32296 by abdo imad last updated on 22/Mar/18 $${let}\:\:{u}_{{n}} =\:\frac{\left({n}+\mathrm{1}\right)^{\alpha} \:\:−{n}^{\alpha} }{{n}^{\alpha−\mathrm{1}} }\:\:{with}\:\alpha>\mathrm{1}\:\:{find}\:{lim}_{{n}\rightarrow\infty} {u}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32291 by abdo imad last updated on 22/Mar/18 $${let}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{n}+{k}}\:{prove}\:{that}\:\mathrm{0}\leqslant{u}_{{n}} \leqslant\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32286 by abdo imad last updated on 22/Mar/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\frac{{e}^{{x}} }{\:\sqrt{\mathrm{1}+{x}}}\:−\mathrm{1}−\frac{{x}}{\mathrm{2}}}{{x}^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32281 by abdo imad last updated on 22/Mar/18 $${calculate}\:{lim}_{{x}\rightarrow\infty} \sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:−\sqrt{{x}^{\mathrm{2}} \:−{x}+\mathrm{1}}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32279 by abdo imad last updated on 22/Mar/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}−{cosx}\right)}\:.\frac{{e}^{{x}} \:−\mathrm{1}}{{x}}\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32278 by abdo imad last updated on 22/Mar/18 $${calculate}\:{lim}_{{x}\rightarrow+\infty} \left({x}−\mathrm{1}\right){cos}\left(\frac{\pi}{{x}}\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97807 by Ar Brandon last updated on 09/Jun/20 $$\mathcal{G}\mathrm{iven}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} ,\:\mathrm{suppose}\:\left(\mathrm{u}_{\mathrm{2n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{u}_{\mathrm{2n}+\mathrm{1}} \right)_{\mathrm{n}\in\mathbb{N}} \\ $$$$\mathrm{converge}\:\mathrm{towards}\:\mathrm{the}\:\mathrm{same}\:\mathrm{limit},\:\mathrm{L}. \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{equally}\:\mathrm{converges}\:\mathrm{to}\:\mathrm{L}. \\ $$ Terms…
Question Number 32255 by abdo imad last updated on 22/Mar/18 $${le}\:{x}>\mathrm{0}\:{and}\:{a}>\mathrm{0}\:{find}\:{lim}_{{x}\rightarrow{a}} \:\frac{{log}_{{a}} \:\left({x}\right)\:−{log}_{{x}} \left({a}\right)}{{sinx}\:−{sina}}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32256 by abdo imad last updated on 22/Mar/18 $$\left.\mathrm{1}\right){let}\:{a}>\mathrm{0}\:{and}\:{x}>\mathrm{0}\:{find}\:{lim}\:_{{x}\rightarrow{a}} \:\frac{{e}^{−{ax}^{\mathrm{2}} } \:−\:{e}^{−{xa}^{\mathrm{2}} } }{{a}^{{x}} \:−{x}^{{a}} }\:. \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow\mathrm{2}} \:\:\:\frac{{e}^{−\mathrm{2}{x}^{\mathrm{2}} } \:−\:{e}^{−\mathrm{4}{x}} }{\mathrm{2}^{{x}} \:−{x}^{\mathrm{2}}…