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Author: Tinku Tara

Question-212834

Question Number 212834 by efronzo1 last updated on 25/Oct/24 $$\:\:\:\:\underbrace{\:} \\ $$ Answered by golsendro last updated on 25/Oct/24 $$\:\:\mathrm{let}\:\begin{cases}{\mathrm{a}=\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{b}=\mathrm{cos}\:\mathrm{x}}\\{\mathrm{c}=\mathrm{sin}\:\mathrm{y}\:,\:\mathrm{d}=\mathrm{cos}\:\mathrm{y}}\end{cases} \\ $$$$\:\:\mathrm{ac}\:+\:\mathrm{bd}\:=\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{y}\right) \\ $$$$\:\:\mid\mathrm{ac}+\mathrm{bd}\mid\:\leqslant\:\mathrm{1}\: \\…

lim-x-1-1-x-x-2-e-x-

Question Number 212798 by MrGaster last updated on 24/Oct/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{\frac{{x}^{\mathrm{2}} }{{e}^{{x}} }} =? \\ $$ Answered by mehdee7396 last updated on 24/Oct/24 $${lim}_{{x}\rightarrow\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)=\mathrm{1}\:\:\:\:\&\:\:\:\:{lim}_{{x}\rightarrow\infty}…