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AllQuestion and Answers: Page 525

Question Number 166296 Answers: 0 Comments: 2

(cos x)^(2022) −(sin x)^(2022) =1 x=?

$$\left(\mathrm{cos}\:{x}\right)^{\mathrm{2022}} −\left(\mathrm{sin}\:{x}\right)^{\mathrm{2022}} =\mathrm{1} \\ $$$${x}=? \\ $$

Question Number 166294 Answers: 0 Comments: 5

f(x)=∫_1 ^x (dt/( (√(t^3 +2t^2 +3)))) (f^(−1) (0))′=?

$$\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{1}} ^{{x}} \:\frac{{dt}}{\:\sqrt{{t}^{\mathrm{3}} +\mathrm{2}{t}^{\mathrm{2}} +\mathrm{3}}} \\ $$$$\:\:\:\left({f}^{−\mathrm{1}} \left(\mathrm{0}\right)\right)'=? \\ $$

Question Number 166291 Answers: 1 Comments: 0

calculer la somme Σ_(n=1) ^(+oo) (1/(n(n+2)))x^n

$${calculer}\:{la}\:{somme} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}{x}^{{n}} \\ $$

Question Number 166284 Answers: 0 Comments: 1

Question Number 166281 Answers: 1 Comments: 0

Question Number 166280 Answers: 1 Comments: 0

Solve for the exact value of ∫_0 ^( ∞) sin(x^2 + x^(−2) ) dx

$$\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\:\infty} \mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{−\mathrm{2}} \right)\:\mathrm{dx} \\ $$

Question Number 166279 Answers: 0 Comments: 0

if y = x^x^x^x find y^′ ?

$${if}\:{y}\:=\:{x}^{{x}^{{x}^{{x}} } } \:{find}\:{y}^{'} \:? \\ $$

Question Number 166273 Answers: 2 Comments: 1

Question Number 166263 Answers: 1 Comments: 0

∫_( −(π/4)) ^( (π/4)) (dx/(cos^2 x (√(9+7 tan ∣x∣)))) dx =?

$$\:\:\:\:\:\:\int_{\:−\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{dx}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{9}+\mathrm{7}\:\mathrm{tan}\:\mid\mathrm{x}\mid}}\:\mathrm{dx}\:=? \\ $$

Question Number 166301 Answers: 2 Comments: 0

∫(x/( (√(1+x^2 +(√((1+x^2 )^3 ))))))dx

$$\int\frac{{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}}{dx} \\ $$

Question Number 166261 Answers: 1 Comments: 1

If four men can dig a piece of land in 2days at eight hours everyday.How many days can two men dig in every six hours perday?

$${If}\:{four}\:{men}\:{can}\:{dig}\:{a}\:{piece}\:{of}\:{land}\:{in}\:\mathrm{2}{days}\:{at}\:{eight}\:{hours}\:{everyday}.{How}\:{many}\:{days}\:{can}\:{two}\:{men}\:{dig}\:{in}\:{every}\:{six}\:{hours}\:{perday}? \\ $$

Question Number 166254 Answers: 1 Comments: 0

Θ=Σ_(n=1) ^∞ (( H_( n) )/(n. (n+1 ))) =^? (π^( 2) /6) −−−−+

$$ \\ $$$$\:\:\:\:\Theta=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{H}_{\:{n}} }{{n}.\:\left({n}+\mathrm{1}\:\right)}\:\:\overset{?} {=}\:\frac{\pi^{\:\mathrm{2}} }{\mathrm{6}} \\ $$$$\:\:\:\:\:−−−−+ \\ $$

Question Number 166252 Answers: 1 Comments: 1

Question Number 166234 Answers: 0 Comments: 0

sin^(−1) (a/(2R))+sin^(−1) (b/(2R))+sin^(−1) (c/(2R))=(π/4) find R n terms of a,b,c.

$$\:\:\mathrm{sin}^{−\mathrm{1}} \frac{{a}}{\mathrm{2}{R}}+\mathrm{sin}^{−\mathrm{1}} \frac{{b}}{\mathrm{2}{R}}+\mathrm{sin}^{−\mathrm{1}} \frac{{c}}{\mathrm{2}{R}}=\frac{\pi}{\mathrm{4}} \\ $$$${find}\:{R}\:{n}\:{terms}\:{of}\:{a},{b},{c}. \\ $$

Question Number 166223 Answers: 0 Comments: 0

Question Number 166258 Answers: 0 Comments: 0

Question Number 166257 Answers: 1 Comments: 2

⌊x⌋⌊2x⌋⌊3x⌋= 6 x=?^

$$ \\ $$$$\:\:\:\lfloor{x}\rfloor\lfloor\mathrm{2}{x}\rfloor\lfloor\mathrm{3}{x}\rfloor=\:\mathrm{6} \\ $$$$\:\:\:\:\:\:\:{x}=\overset{} {?}\: \\ $$

Question Number 166212 Answers: 1 Comments: 0

x, y , z ∈R^( +) and x≥y≥z and x^2 +y^( 2) +z^( 2) ≥ 2xy +2xz+2yz Find Min((x/z) )=?

$$ \\ $$$$\:\:\:{x},\:{y}\:,\:{z}\:\in\mathbb{R}^{\:+} \:{and}\:\:{x}\geqslant{y}\geqslant{z} \\ $$$$\:\:\:\:{and}\:\: \\ $$$$\:\:\:\:{x}^{\mathrm{2}} +{y}^{\:\mathrm{2}} +{z}^{\:\mathrm{2}} \geqslant\:\mathrm{2}{xy}\:+\mathrm{2}{xz}+\mathrm{2}{yz} \\ $$$$\:\:\:\:\:\:\mathrm{F}{ind}\:\:\:\:\:\mathrm{M}{in}\left(\frac{{x}}{{z}}\:\right)=? \\ $$

Question Number 166210 Answers: 1 Comments: 0

Question Number 166208 Answers: 2 Comments: 1

Question Number 166246 Answers: 1 Comments: 0

Question Number 166195 Answers: 3 Comments: 0

Question Number 166192 Answers: 1 Comments: 0

∫ (dx/(5+4sin x)) =?

$$\:\:\:\:\int\:\frac{{dx}}{\mathrm{5}+\mathrm{4sin}\:{x}}\:=? \\ $$

Question Number 166191 Answers: 1 Comments: 0

∫^( (π/2)) _(−(π/2)) ((sin x)/(x^4 +x^2 +1)) dx=?

$$\:\:\:\:\:\:\:\underset{−\frac{\pi}{\mathrm{2}}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}=? \\ $$

Question Number 166186 Answers: 2 Comments: 0

if sinθ = (1/2) find cosθ

$${if}\:{sin}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:{cos}\theta \\ $$

Question Number 166182 Answers: 2 Comments: 0

calculer la primitive de ∫(t^2 /((1+t^2 )^2 ))dt

$${calculer}\:{la}\:{primitive}\:{de} \\ $$$$\int\frac{{t}^{\mathrm{2}} }{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$

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