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Question Number 147353 Answers: 0 Comments: 0

Question Number 147349 Answers: 2 Comments: 2

lim_(x→0) ((x(1−cos x))/(x^2 +x−e^x sin x)) =?

$$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{e}^{\mathrm{x}} \:\mathrm{sin}\:\mathrm{x}}\:=? \\ $$

Question Number 147346 Answers: 1 Comments: 0

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Question Number 147322 Answers: 1 Comments: 3

Question Number 147321 Answers: 0 Comments: 0

Question Number 147320 Answers: 1 Comments: 0

16x+9y=1 find x and y

$$\mathrm{16}{x}+\mathrm{9}{y}=\mathrm{1} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$

Question Number 147312 Answers: 1 Comments: 0

Question Number 147310 Answers: 1 Comments: 1

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Question Number 147303 Answers: 1 Comments: 0

If log_6 30 = a, log_(15) 24 = b, evaluate log_(12) 60

$$\mathrm{If}\:\:\:\:\:\mathrm{log}_{\mathrm{6}} \mathrm{30}\:\:=\:\:\mathrm{a},\:\:\:\:\:\:\mathrm{log}_{\mathrm{15}} \mathrm{24}\:\:\:=\:\:\:\mathrm{b},\:\:\:\:\:\:\:\mathrm{evaluate}\:\:\:\:\:\:\mathrm{log}_{\mathrm{12}} \mathrm{60} \\ $$

Question Number 147302 Answers: 1 Comments: 0

P_a (z)=z^(2n) −2z^n cosa+1 montrer que p_a (z)=Π_(k=0) ^(n−1) (z^2 −2zcos((a/π)+((2kπ)/n))+1)

$${P}_{{a}} \left({z}\right)={z}^{\mathrm{2}{n}} −\mathrm{2}{z}^{{n}} {cosa}+\mathrm{1} \\ $$$${montrer}\:{que}\:\:{p}_{{a}} \left(\mathrm{z}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({z}^{\mathrm{2}} −\mathrm{2}{zcos}\left(\frac{{a}}{\pi}+\frac{\mathrm{2}{k}\pi}{{n}}\right)+\mathrm{1}\right) \\ $$

Question Number 147294 Answers: 1 Comments: 0

Σ(((−1)^n )/n^4 )=?

$$\Sigma\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} }=? \\ $$

Question Number 147290 Answers: 0 Comments: 0

Question Number 147287 Answers: 2 Comments: 0

...Advanced Calculus... Calculate :: { (( i :: I := ∫_0 ^( 1) ln(x).ln(1+x) dx)),(( ii :: J := ∫_0 ^( 1) Li_( 2) ( 1− x^( 2) ) =?)) :} Note:: Li_2 (x) = Σ_(n=1) ^( ∞) (x^( n) /n^( 2) ) ........ ■ .... m.n....

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{Advanced}\:\:\mathrm{Calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{C}{alculate}\:::\:\:\:\:\begin{cases}{\:\:\mathrm{i}\:::\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{ln}\left(\mathrm{x}\right).\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\:\mathrm{dx}}\\{\:\:\mathrm{ii}\:::\:\:\:\:\:\mathrm{J}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \left(\:\mathrm{1}−\:\mathrm{x}^{\:\mathrm{2}} \right)\:=?}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Note}::\:\:\:\mathrm{Li}_{\mathrm{2}} \:\left(\mathrm{x}\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{\:\infty} {\sum}}\:\frac{\mathrm{x}^{\:{n}} }{{n}^{\:\mathrm{2}} }\:\:\:\:........\:\blacksquare\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:....\:\mathrm{m}.\mathrm{n}.... \\ $$$$ \\ $$

Question Number 147285 Answers: 1 Comments: 0

Q: if , g (x) = 2^( ⌊x⌋ + x) , D_( g) = [0, ∞ ) then : g^( −1) (x )=? D_g^( −1) = ?

$$\:\:\:\mathrm{Q}: \\ $$$$ \\ $$$$\:{if}\:,\:\:\:{g}\:\left({x}\right)\:=\:\mathrm{2}^{\:\lfloor{x}\rfloor\:+\:{x}} \:\:,\:\mathrm{D}_{\:{g}} =\:\left[\mathrm{0},\:\infty\:\right) \\ $$$$\:\:\:\:\:\:{then}\:: \\ $$$$\:\:\:\:\:\:\:\:{g}^{\:−\mathrm{1}} \:\left({x}\:\right)=? \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{D}_{{g}^{\:−\mathrm{1}} } =\:? \\ $$$$ \\ $$

Question Number 147278 Answers: 0 Comments: 0

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Question Number 147275 Answers: 1 Comments: 0

f(x)=∫_0 ^x e^(t−(t^2 /2)) dt show that ∫_0 ^1 f(t)dt=(√e)−1

$${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{{t}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}} {dt}\: \\ $$$${show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}=\sqrt{{e}}−\mathrm{1} \\ $$

Question Number 147272 Answers: 1 Comments: 0

Question Number 147262 Answers: 2 Comments: 0

...# Calculus #... I := ∫_0 ^( 1) Li_( 2) (x^( 2) ) dx = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...#\:\:\mathrm{Calculus}\:#... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \:\left({x}^{\:\mathrm{2}} \right)\:{dx}\:=\:? \\ $$$$ \\ $$$$ \\ $$

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Question Number 147259 Answers: 2 Comments: 0

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