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Category: Algebra

lim-x-sin1-1-x-2-1-cosx-

Question Number 200795 by mathlove last updated on 23/Nov/23 $$\underset{{x}\rightarrow{sin}\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{cosx}}=? \\ $$ Answered by witcher3 last updated on 23/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{is}\:\:\mathrm{defined}\:\mathrm{in}\:\mathrm{sin}\left(\mathrm{1}\right) \\ $$$$…

sinx-cosx-tgx-x-

Question Number 200788 by hardmath last updated on 23/Nov/23 $$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 23/Nov/23 $${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}}…

1-a-8-b-5-6-a-b-max-

Question Number 200716 by hardmath last updated on 22/Nov/23 $$\mathrm{1}.\: \\ $$$$\frac{{a}}{\mathrm{8}}\:+\:\frac{{b}}{\mathrm{5}}\:=\:\mathrm{6}\:\:\:\Rightarrow\:\:\:\left({a}+{b}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$ Answered by AST last updated on 22/Nov/23 $$\mathrm{5}{a}+\mathrm{8}{b}=\mathrm{240}\Rightarrow{a}=\frac{\mathrm{240}−\mathrm{8}{b}}{\mathrm{5}} \\ $$$${remains}\:{to}\:{find}\:\left({a}+{b}\right)_{{max}}…