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Question Number 146307 Answers: 1 Comments: 0

S_n =Σ_(k=1) ^n (( 1)/(k (k+2)k+4))) lim_( n→∞) ( S_( n) ) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{S}_{{n}} \:=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\:\mathrm{1}}{\left.{k}\:\left({k}+\mathrm{2}\right){k}+\mathrm{4}\right)} \\ $$$$\:\:\:\:\:\:\:\:{lim}_{\:{n}\rightarrow\infty} \:\left(\:\:\mathrm{S}_{\:{n}} \:\right)\:=\:? \\ $$

Question Number 146303 Answers: 2 Comments: 4

Question Number 146300 Answers: 1 Comments: 0

Question Number 146290 Answers: 0 Comments: 5

Question Number 146285 Answers: 3 Comments: 2

∫ sin(2x - (π/4)) dx = ?

$$\int\:{sin}\left(\mathrm{2}{x}\:-\:\frac{\pi}{\mathrm{4}}\right)\:{dx}\:=\:? \\ $$

Question Number 146277 Answers: 1 Comments: 0

∫cos(2x)dx=?

$$\int{cos}\left(\mathrm{2}{x}\right){dx}=? \\ $$

Question Number 146272 Answers: 1 Comments: 3

log_x (x^2 + 1) ≤ 1

$${log}_{\boldsymbol{{x}}} \left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\leqslant\:\mathrm{1} \\ $$

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

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

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