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AllQuestion and Answers: Page 251

Question Number 196406 Answers: 1 Comments: 0

Σ_(n,m=1) ^∞ (((−1)^(n+m) nm)/((n+m)^2 ))=?

$$\underset{{n},{m}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+{m}} {nm}}{\left({n}+{m}\right)^{\mathrm{2}} }=? \\ $$

Question Number 196401 Answers: 3 Comments: 0

if y=sin x find (d^2 /dy^2 )cos^7 x

$$\mathrm{if}\:{y}=\mathrm{sin}\:{x}\: \\ $$$$\mathrm{find}\:\frac{\boldsymbol{{d}}^{\mathrm{2}} }{\boldsymbol{{d}}{y}^{\mathrm{2}} }\mathrm{co}\boldsymbol{{s}}^{\mathrm{7}} \boldsymbol{{x}} \\ $$

Question Number 196399 Answers: 1 Comments: 0

a/ lim_((x,y)→(0,2)) (1+xy)^(2/(x^2 +xy)) b/ lim_((x,y)→(0,0)) (x^2 +y^2 )sin((1/(xy))) c/lim_((x,y)→(∞,∞)) (x^2 +y^2 )e^(−(x+y))

$${a}/\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{2}\right)} {\mathrm{lim}}\:\left(\mathrm{1}+{xy}\right)^{\frac{\mathrm{2}}{{x}^{\mathrm{2}} +{xy}}} \\ $$$${b}/\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){sin}\left(\frac{\mathrm{1}}{{xy}}\right) \\ $$$${c}/\underset{\left({x},{y}\right)\rightarrow\left(\infty,\infty\right)} {\mathrm{lim}}\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){e}^{−\left({x}+{y}\right)} \\ $$

Question Number 196396 Answers: 0 Comments: 1

lim_(n→∞) [(−1)^n ∙n]=?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\left(−\mathrm{1}\right)^{{n}} \centerdot{n}\right]=? \\ $$

Question Number 196395 Answers: 0 Comments: 1

Question Number 196394 Answers: 1 Comments: 0

If f(x)=∫^( x) _( 0) e^(−f(t)) dt Determine f(x)

$$\mathrm{If}\:\:{f}\left({x}\right)=\underset{\:\mathrm{0}} {\int}^{\:{x}} {e}^{−{f}\left({t}\right)} {dt} \\ $$$$\mathrm{Determine}\:{f}\left({x}\right) \\ $$

Question Number 196388 Answers: 2 Comments: 0

Question Number 196375 Answers: 1 Comments: 1

∫(dx/(x(x^4 −1)))

$$\int\frac{{dx}}{{x}\left({x}^{\mathrm{4}} −\mathrm{1}\right)} \\ $$

Question Number 196398 Answers: 0 Comments: 2

y=f(x) Give: xy−y′=x^2 Find y=¿

$${y}={f}\left({x}\right) \\ $$$${Give}:\:{xy}−{y}'={x}^{\mathrm{2}} \\ $$$${Find}\:{y}=¿ \\ $$

Question Number 196364 Answers: 1 Comments: 0

xp(x)=x^3 −2x^2 +x−a p(−1)=?

$${xp}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}−{a} \\ $$$${p}\left(−\mathrm{1}\right)=? \\ $$

Question Number 196360 Answers: 2 Comments: 1

Question Number 196355 Answers: 2 Comments: 1

log_5 (√(5(√(5(√(5(√(5.....)))))) ))= ?

$$\mathrm{log}_{\mathrm{5}} \sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}.....}}}\:}=\:? \\ $$

Question Number 196352 Answers: 0 Comments: 0

Question Number 196351 Answers: 0 Comments: 0

Question Number 196347 Answers: 1 Comments: 3

(19^((20^(21) )) ) factorial plz hepl me so soon

$$\left(\mathrm{1}\overset{\left(\mathrm{2}\overset{\mathrm{21}} {\mathrm{0}}\right)} {\mathrm{9}}\right)\:\boldsymbol{\mathrm{factorial}}\:\boldsymbol{\mathrm{plz}}\:\boldsymbol{\mathrm{hepl}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{soon}} \\ $$

Question Number 196358 Answers: 0 Comments: 2

Question Number 196343 Answers: 2 Comments: 0

find the minimum value of f(x) f(x) = (√(x^2 −2x +5)) + (√(4x^2 −4x +10 ))

$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:+\mathrm{5}}\:\:+\:\:\sqrt{\mathrm{4x}^{\mathrm{2}} \:−\mathrm{4x}\:+\mathrm{10}\:} \\ $$

Question Number 196337 Answers: 1 Comments: 0

Question Number 196327 Answers: 2 Comments: 0

calcul la somme suivante: lim_(n→+∞) Σ_(k=n) ^(2n) sin((𝛑/k)) elrochi

$$\boldsymbol{{calcul}}\:\boldsymbol{{la}}\:\boldsymbol{{somme}}\:\boldsymbol{{suivante}}: \\ $$$$\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\:\underset{\boldsymbol{{k}}=\boldsymbol{{n}}} {\overset{\mathrm{2}\boldsymbol{{n}}} {\sum}}\boldsymbol{{sin}}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{{k}}}\right) \\ $$$$\:\:\boldsymbol{{elrochi}} \\ $$

Question Number 196325 Answers: 1 Comments: 0

Σ_(n=0) ^∞ arg(n^2 +n+1+i)= π/2

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)=\:\pi/\mathrm{2}\: \\ $$

Question Number 196324 Answers: 2 Comments: 0

Question Number 196322 Answers: 1 Comments: 0

f^((1/2)) (x)= (d/dx)(∫_0 ^x ((f(x−t))/( (√(πt))))dt) Prove that (f^((1/2)) )^((1/2)) = f ′ At least for f = 1 then f = x

$$\:\:\:\:{f}^{\left(\mathrm{1}/\mathrm{2}\right)} \left({x}\right)=\:\frac{{d}}{{dx}}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{f}\left({x}−{t}\right)}{\:\sqrt{\pi{t}}}{dt}\right) \\ $$$${Prove}\:\:{that}\:\:\:\:\left({f}^{\left(\mathrm{1}/\mathrm{2}\right)} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} =\:{f}\:'\:\:\:\: \\ $$$${At}\:\:{least}\:\:{for}\:\:{f}\:=\:\:\mathrm{1}\:\:{then}\:\:{f}\:=\:{x} \\ $$

Question Number 196321 Answers: 1 Comments: 0

lim_(n→+∞) sin(2π(√(n^2 +1 )) ) = 0 lim_(n→+∞) arg(n^2 +n+1+i) = 0

$$\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{sin}\left(\mathrm{2}\pi\sqrt{{n}^{\mathrm{2}} +\mathrm{1}\:}\:\right)\:=\:\mathrm{0} \\ $$$$\:\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:\:{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)\:=\:\mathrm{0} \\ $$

Question Number 196320 Answers: 1 Comments: 0

If a regular n−polygon can be divided into n identical equilateral triangles then n=6

$$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$

Question Number 196311 Answers: 0 Comments: 0

Question Number 196309 Answers: 2 Comments: 1

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