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AllQuestion and Answers: Page 206

Question Number 201388 Answers: 2 Comments: 0

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2023^(2023) = ... (mod 13)

$$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:=\:...\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$

Question Number 201351 Answers: 2 Comments: 0

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Question Number 201341 Answers: 2 Comments: 0

if a>0 and m≥0 ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )^2 ))dx=?

$${if}\:{a}>\mathrm{0}\:\:{and}\:\:{m}\geqslant\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}=? \\ $$

Question Number 201463 Answers: 1 Comments: 0

a = constant number: if ∫x ∙ f(x) dx = x^3 - x^2 + 4x - (a/5) find f(2) = ?

$$\mathrm{a}\:=\:\mathrm{constant}\:\mathrm{number}: \\ $$$$\mathrm{if}\:\:\:\int\mathrm{x}\:\centerdot\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:-\:\frac{\mathrm{a}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 201462 Answers: 1 Comments: 0

Find: ∫_0 ^( 𝛑) (√(1 - 4 sin^2 (x/2) cos^2 (x/2))) dx = ?

$$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \:\sqrt{\mathrm{1}\:-\:\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{cos}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 201456 Answers: 1 Comments: 0

Question Number 201460 Answers: 1 Comments: 0

Find the smallest positive period of the function: y = ∣ tan 2x ∣ + ∣ cot 2x ∣

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{function}: \\ $$$$\mathrm{y}\:=\:\mid\:\mathrm{tan}\:\mathrm{2x}\:\mid\:\:+\:\:\mid\:\mathrm{cot}\:\mathrm{2x}\:\mid \\ $$

Question Number 201332 Answers: 1 Comments: 0

calcul : 1. lim_(n→+∞ ) ((sin(n^2 )−cos(n^3 ))/n) 2. lim_(n→+∞) ^n (√(3−sin(n^2 ))) 3. lim_(n→+∞) (n/(n+1)) e^(i((nπ)/3))

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:{calcul}\:: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{1}.\:\:\:\:{lim}_{{n}\rightarrow+\infty\:} \frac{{sin}\left({n}^{\mathrm{2}} \right)−{cos}\left({n}^{\mathrm{3}} \right)}{{n}}\: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{2}.\:\:\:\:\:{lim}_{{n}\rightarrow+\infty} \:^{{n}} \sqrt{\mathrm{3}−{sin}\left({n}^{\mathrm{2}} \right)} \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{3}.\:\:\:\:\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{n}}{{n}+\mathrm{1}}\:{e}^{{i}\frac{{n}\pi}{\mathrm{3}}} \: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201329 Answers: 1 Comments: 0

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