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Question Number 148441 Answers: 0 Comments: 0

Σ_(k=1) ^∞ Σ_(m=1) ^n ((n(m−1))/((nk+m−1)(nk+m)))=?

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{m}−\mathrm{1}\right)}{\left(\mathrm{nk}+\mathrm{m}−\mathrm{1}\right)\left(\mathrm{nk}+\mathrm{m}\right)}=? \\ $$

Question Number 148439 Answers: 3 Comments: 0

lim_(x→2) (((√(x+2)) ((x+6))^(1/3) −x^2 )/(x−2)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{6}}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}−\mathrm{2}}\:=? \\ $$

Question Number 148483 Answers: 1 Comments: 0

Soit f une fonction continu sur R et non identiquement nulle, ∀ x,x′∈R, f(x−x′)+f(x+x′)=2f(x)f(x′) montrer que: f(0)=1 et f(x)=f(−x)..

$$\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{fonction}\:\mathrm{continu}\:\mathrm{sur}\:\mathbb{R} \\ $$$$\mathrm{et}\:\mathrm{non}\:\mathrm{identiquement}\:\mathrm{nulle}, \\ $$$$\forall\:\mathrm{x},\mathrm{x}'\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}−\mathrm{x}'\right)+\mathrm{f}\left(\mathrm{x}+\mathrm{x}'\right)=\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{x}'\right) \\ $$$$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{et}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(−\mathrm{x}\right).. \\ $$

Question Number 148428 Answers: 1 Comments: 0

Question Number 148427 Answers: 2 Comments: 0

Question Number 148421 Answers: 0 Comments: 0

lim_(x→∞) ((cos(x) - x!)/(3^x - 4^x )) = ?

$$\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}}\frac{{cos}\left({x}\right)\:-\:{x}!}{\mathrm{3}^{\boldsymbol{{x}}} \:-\:\mathrm{4}^{\boldsymbol{{x}}} }\:=\:? \\ $$

Question Number 148418 Answers: 1 Comments: 0

Find the natural roots of the equation x^2 - 51y^2 = 1

$${Find}\:{the}\:{natural}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{51}{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$

Question Number 148417 Answers: 0 Comments: 0

Question Number 148408 Answers: 2 Comments: 0

∫x^5 e^x^2 dx Help please!

$$\int{x}^{\mathrm{5}} {e}^{{x}^{\mathrm{2}} } {dx} \\ $$$${Help}\:{please}! \\ $$

Question Number 148404 Answers: 0 Comments: 0

Question Number 148403 Answers: 1 Comments: 0

Question Number 148397 Answers: 0 Comments: 0

Question Number 148395 Answers: 1 Comments: 0

x^x = 64 ⇒ x = ?

$$\boldsymbol{{x}}^{\boldsymbol{{x}}} \:=\:\mathrm{64} \\ $$$$\Rightarrow\:\boldsymbol{{x}}\:=\:? \\ $$

Question Number 148388 Answers: 1 Comments: 0

cos40°(1 - 2cos80°) = ?

$${cos}\mathrm{40}°\left(\mathrm{1}\:-\:\mathrm{2}{cos}\mathrm{80}°\right)\:=\:? \\ $$

Question Number 148382 Answers: 0 Comments: 0

0.8%×544

$$\mathrm{0}.\mathrm{8\%}×\mathrm{544} \\ $$

Question Number 148381 Answers: 0 Comments: 0

Question Number 148376 Answers: 1 Comments: 0

∫_1 ^∞ x^i lnxdx i^2 =−1

$$\int_{\mathrm{1}} ^{\infty} {x}^{{i}} {lnxdx}\:\:\:\:\:\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$

Question Number 148374 Answers: 0 Comments: 0

Solve the equation on the set of real number: (8/( (√(6 - 2z)))) + (2/( (√z))) = z^2 - 2z + 7

$${Solve}\:{the}\:{equation}\:{on}\:{the}\:{set}\:{of}\:{real} \\ $$$${number}:\:\:\:\frac{\mathrm{8}}{\:\sqrt{\mathrm{6}\:-\:\mathrm{2}{z}}}\:+\:\frac{\mathrm{2}}{\:\sqrt{{z}}}\:=\:{z}^{\mathrm{2}} \:-\:\mathrm{2}{z}\:+\:\mathrm{7} \\ $$

Question Number 148375 Answers: 0 Comments: 0

∫_1 ^∞ sin(x+lnx)dx

$$\int_{\mathrm{1}} ^{\infty} {sin}\left({x}+{lnx}\right){dx} \\ $$

Question Number 148372 Answers: 1 Comments: 0

calculate ∫_γ z^3 e^(1/z^2 ) dz with γ(t)=3e^(it) and t∈[0,2π]

$$\mathrm{calculate}\:\int_{\gamma} \mathrm{z}^{\mathrm{3}} \:\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\mathrm{3e}^{\mathrm{it}} \:\:\:\:\mathrm{and}\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$

Question Number 148371 Answers: 1 Comments: 0

calculate ∫_γ ze^(2/z^2 ) dz with γ(t)=(√3)e^(it) t∈[0,2π]

$$\mathrm{calculate}\:\int_{\gamma} \mathrm{ze}^{\frac{\mathrm{2}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\sqrt{\mathrm{3}}\mathrm{e}^{\mathrm{it}} \:\:\:\:\:\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$

Question Number 148368 Answers: 0 Comments: 0

Question Number 148356 Answers: 0 Comments: 2

Question Number 148362 Answers: 0 Comments: 0

Show that the equation 4xy-x-y=z^2 has no solution in natural numbers.

$${Show}\:{that}\:{the}\:{equation}\:\:\mathrm{4}{xy}-{x}-{y}={z}^{\mathrm{2}} \\ $$$${has}\:{no}\:{solution}\:{in}\:{natural}\:{numbers}. \\ $$

Question Number 148350 Answers: 0 Comments: 1

(((1/2)+(1/3)+....+(1/9))/((9/1)+(8/2)+...+(1/9)))=?

$$\frac{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+....+\frac{\mathrm{1}}{\mathrm{9}}}{\frac{\mathrm{9}}{\mathrm{1}}+\frac{\mathrm{8}}{\mathrm{2}}+...+\frac{\mathrm{1}}{\mathrm{9}}}=? \\ $$

Question Number 148341 Answers: 0 Comments: 0

Solve the inequality: (5 - ∣x∣ )^(− (1/3)) ∙ (x^2 - 4) < 0

$${Solve}\:{the}\:{inequality}: \\ $$$$\left(\mathrm{5}\:-\:\mid{x}\mid\:\right)^{−\:\frac{\mathrm{1}}{\mathrm{3}}} \:\centerdot\:\left({x}^{\mathrm{2}} \:-\:\mathrm{4}\right)\:<\:\mathrm{0} \\ $$

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