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Calculate-a-lim-x-x-1-x-1-x-2-b-lim-x-0-2-1-x-1-2-1-x-1-

Question Number 160917 by LEKOUMA last updated on 09/Dec/21 $${Calculate} \\ $$$$\left.{a}\right)\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{{x}^{\mathrm{2}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}} \\ $$ Answered by jama last…

Calculate-1-lim-x-0-x-1-2x-1-x-2-lim-x-a-sin-x-sin-a-1-x-a-

Question Number 160900 by LEKOUMA last updated on 08/Dec/21 $${Calculate} \\ $$$$\left.\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}\right)^{{x}^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}}\right)^{\frac{\mathrm{1}}{{x}−{a}}} \\ $$ Commented by cortano last updated on…

Prove-the-convergence-of-each-of-the-following-sequence-i-n-1-n-n-1-ii-1-2-1-n-n-1-iii-n-1-n-n-1-

Question Number 29607 by tawa tawa last updated on 10/Feb/18 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$\left(\mathrm{i}\right)\:\:\left\{\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\:\:\:\:\:\:\left(\mathrm{ii}\right)\:\:\:\left\{\frac{\mathrm{1}}{\:\sqrt[{\mathrm{n}}]{\mathrm{2}}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\:\:\:\:\left(\mathrm{iii}\right)\:\:\:\:\left\{\frac{\mathrm{n}\:+\:\mathrm{1}}{\mathrm{n}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$ Terms of Service Privacy Policy…