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Question Number 146318 Answers: 1 Comments: 4

if arg (((z−i)/i))=2 find Imz + Rez = ?

$${if}\:\:\:{arg}\:\left(\frac{{z}−{i}}{{i}}\right)=\mathrm{2} \\ $$$${find}\:\:\:{Imz}\:+\:{Rez}\:=\:? \\ $$

Question Number 146317 Answers: 0 Comments: 0

Question Number 146316 Answers: 2 Comments: 0

Question Number 146263 Answers: 2 Comments: 0

lim_(x→−∞) (−2x+1−(√(4x^2 −5x+8)))=?

$$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(−\mathrm{2}{x}+\mathrm{1}−\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{8}}\right)=? \\ $$

Question Number 146261 Answers: 1 Comments: 0

4 cos (50°) - (1/(sin (20°))) = ?

$$\mathrm{4}\:{cos}\:\left(\mathrm{50}°\right)\:-\:\frac{\mathrm{1}}{{sin}\:\left(\mathrm{20}°\right)}\:=\:? \\ $$

Question Number 146260 Answers: 1 Comments: 0

solve y^(′′) −2y^′ +y =e^(−x) sinx

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{2y}^{'} \:+\mathrm{y}\:=\mathrm{e}^{−\mathrm{x}} \mathrm{sinx} \\ $$

Question Number 146253 Answers: 2 Comments: 0

(4x^4 - 2x^2 + 17)_(max) = ?

$$\left(\mathrm{4}{x}^{\mathrm{4}} \:-\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{17}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$

Question Number 146250 Answers: 0 Comments: 1

I_k =∫_0 ^(kΠ) e^x^2 sin x dx then find relation between I_1 ,I_2 ,I_3

$${I}_{{k}} =\underset{\mathrm{0}} {\overset{{k}\Pi} {\int}}{e}^{{x}^{\mathrm{2}} } \mathrm{sin}\:{x}\:{dx}\:{then}\:{find}\:{relation}\: \\ $$$${between}\:{I}_{\mathrm{1}} ,{I}_{\mathrm{2}} ,{I}_{\mathrm{3}} \\ $$

Question Number 146366 Answers: 1 Comments: 0

Question Number 146365 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(x^2 +4))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx} \\ $$

Question Number 146244 Answers: 2 Comments: 0

((√5) - 2)^((2x^2 -1)/2) = ((√5) + 2)^((3x-7)/4) ⇒ x=?

$$\left(\sqrt{\mathrm{5}}\:-\:\mathrm{2}\right)^{\frac{\mathrm{2}{x}^{\mathrm{2}} -\mathrm{1}}{\mathrm{2}}} \:\:=\:\left(\sqrt{\mathrm{5}}\:+\:\mathrm{2}\right)^{\frac{\mathrm{3}{x}-\mathrm{7}}{\mathrm{4}}} \:\:\Rightarrow\:\:{x}=? \\ $$

Question Number 146242 Answers: 1 Comments: 0

4 sin(50°) - (1/(cos(20°))) = ?

$$\mathrm{4}\:{sin}\left(\mathrm{50}°\right)\:-\:\frac{\mathrm{1}}{{cos}\left(\mathrm{20}°\right)}\:=\:? \\ $$

Question Number 146236 Answers: 1 Comments: 0

∫ ((3x + 1)/x) dx = ?

$$\int\:\frac{\mathrm{3}{x}\:+\:\mathrm{1}}{{x}}\:{dx}\:=\:? \\ $$

Question Number 146235 Answers: 2 Comments: 0

if arg z_1 = ((4π)/3) and arg z_1 ^2 ∙ z = ((7π)/6) find arg z = ?

$${if}\:\:\:{arg}\:{z}_{\mathrm{1}} \:=\:\frac{\mathrm{4}\pi}{\mathrm{3}}\:\:\:{and}\:\:\:{arg}\:{z}_{\mathrm{1}} ^{\mathrm{2}} \:\centerdot\:{z}\:=\:\frac{\mathrm{7}\pi}{\mathrm{6}} \\ $$$${find}\:\:\:{arg}\:{z}\:=\:? \\ $$

Question Number 146233 Answers: 1 Comments: 1

Question Number 146230 Answers: 1 Comments: 0

(1/(cos^2 (x))) - 1 + (1/(cos(x))) = 1 ⇒ x=?

$$\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}\:-\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=\:\mathrm{1}\:\Rightarrow\:{x}=? \\ $$

Question Number 146227 Answers: 2 Comments: 0

tg^2 (x) - (1/(cos(x))) = 1 ⇒ x=?

$${tg}^{\mathrm{2}} \left({x}\right)\:-\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=\:\mathrm{1}\:\Rightarrow\:{x}=? \\ $$

Question Number 146224 Answers: 2 Comments: 0

Question Number 146202 Answers: 3 Comments: 0

∫((lnx)/(x−1))dx=....??? La primitive

$$\int\frac{{lnx}}{{x}−\mathrm{1}}{dx}=....??? \\ $$$${La}\:{primitive} \\ $$

Question Number 146201 Answers: 1 Comments: 0

Solve for natural numbers the equation: 3x^2 + 15y^2 = 5z^2 + t^2

$${Solve}\:{for}\:{natural}\:{numbers}\:{the}\:{equation}: \\ $$$$\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{15}{y}^{\mathrm{2}} \:=\:\mathrm{5}{z}^{\mathrm{2}} \:+\:{t}^{\mathrm{2}} \\ $$

Question Number 146215 Answers: 3 Comments: 0

∫ (dx/(x(√(x^2 −4)))) = ?

$$\int\:\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:=\:? \\ $$

Question Number 146196 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)^4 (x+3)^5 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{4}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 146197 Answers: 2 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^3 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 146194 Answers: 1 Comments: 0

calculate Σ_(n=1) ^∞ (1/(n^3 5^n ))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \mathrm{5}^{\mathrm{n}} } \\ $$

Question Number 146193 Answers: 2 Comments: 0

solve y^(′′) −y^′ + y=xe^(−x)

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\:\mathrm{y}=\mathrm{xe}^{−\mathrm{x}} \\ $$

Question Number 146183 Answers: 1 Comments: 1

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