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let p(x)=(1+ix+x^2 )^n −(1−ix +x^2 )^n 1) determine roots of p(x) 2) find p(x) at form Σ a_i x^i 3)ddtermne p(x) at form arctan 4) factorize p(x) inside C[x] 5) calculate ∫_0 ^1 p(x)dxand ∫_1 ^∞ (dx/(p(x)))

$$\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} −\left(\mathrm{1}−\mathrm{ix}\:+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{determine}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\Sigma\:\mathrm{a}_{\mathrm{i}} \:\mathrm{x}^{\mathrm{i}} \\ $$$$\left.\mathrm{3}\right)\mathrm{ddtermne}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\mathrm{arctan} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{5}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{p}\left(\mathrm{x}\right)\mathrm{dxand}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\mathrm{p}\left(\mathrm{x}\right)} \\ $$

Question Number 95832 Answers: 2 Comments: 0

find without using l′hopital lim_(x→2) ((e^(2−x) −1)/(x^2 −4))

$${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{{e}^{\mathrm{2}−{x}} −\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$

Question Number 95830 Answers: 2 Comments: 0

Question Number 95868 Answers: 1 Comments: 1

5^(10) (mod 11)=?

$$\mathrm{5}^{\mathrm{10}} \left({mod}\:\mathrm{11}\right)=? \\ $$

Question Number 95801 Answers: 2 Comments: 0

2y′′−y^′ =1; y(0) = 0 ; y′(0)=1

$$\mathrm{2y}''−\mathrm{y}^{'} =\mathrm{1};\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:;\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{1} \\ $$

Question Number 95800 Answers: 1 Comments: 2

if f(0)=1 f(1)=2 and ∫_0 ^1 f(x) dx=3 than ∫_0 ^1 x f(x) dx = ? a. 1 b. −1 c. 2 d. −2

$${if}\:\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{2}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\:{dx}=\mathrm{3}\: \\ $$$${than}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}\:{f}\left({x}\right)\:{dx}\:=\:? \\ $$$$ \\ $$$${a}.\:\mathrm{1} \\ $$$${b}.\:−\mathrm{1} \\ $$$${c}.\:\mathrm{2} \\ $$$${d}.\:−\mathrm{2} \\ $$$$ \\ $$

Question Number 95789 Answers: 1 Comments: 1

Find the semi−interquartile range of of the following numbers: 15, 10, 9, 15, 15, 8, 10, 11, 8, 12, 11, 14, 9 and 15

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{semi}−\mathrm{interquartile}\:\mathrm{range}\:\mathrm{of}\: \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{numbers}: \\ $$$$\:\mathrm{15},\:\mathrm{10},\:\mathrm{9},\:\mathrm{15},\:\mathrm{15},\:\mathrm{8},\:\mathrm{10},\:\mathrm{11},\:\mathrm{8},\:\mathrm{12},\:\mathrm{11},\:\mathrm{14}, \\ $$$$\:\mathrm{9}\:\mathrm{and}\:\mathrm{15} \\ $$

Question Number 95786 Answers: 1 Comments: 2

let f(x) =(1/x)ln(1+2x) 1) calculate f^((n)) (x)and f^((n)) (1) 2)developp f at integr serie at x_0 =1 3)developp f at integr serie at x_0 =0

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{x}}\mathrm{ln}\left(\mathrm{1}+\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1} \\ $$$$\left.\mathrm{3}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie}\:\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{0} \\ $$

Question Number 95785 Answers: 0 Comments: 0

calculate ∫_0 ^(π/2) (ln(cosx))^3 dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{ln}\left(\mathrm{cosx}\right)\right)^{\mathrm{3}} \:\mathrm{dx} \\ $$

Question Number 95784 Answers: 0 Comments: 0

calculate Σ_(n=1) ^∞ (H_n /n^2 ) H_n =Σ_(k=1) ^n (1/k)

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{H}_{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{H}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{k}} \\ $$

Question Number 95782 Answers: 0 Comments: 2

it looks version 2.077 has a problem. for very long loading

$$\mathrm{it}\:\mathrm{looks}\:\mathrm{version}\:\mathrm{2}.\mathrm{077}\:\mathrm{has}\:\mathrm{a}\: \\ $$$$\mathrm{problem}.\:\:\mathrm{for}\:\mathrm{very}\:\mathrm{long}\:\mathrm{loading} \\ $$

Question Number 95780 Answers: 0 Comments: 0

Question Number 95779 Answers: 2 Comments: 0

if plane 3x+4y+tz=2 and kx+6y+5z−2=0 are parallel. find the value of k and t

$$\mathrm{if}\:\mathrm{plane}\:\mathrm{3x}+\mathrm{4y}+\mathrm{tz}=\mathrm{2}\:\mathrm{and}\: \\ $$$$\mathrm{kx}+\mathrm{6y}+\mathrm{5z}−\mathrm{2}=\mathrm{0}\:\mathrm{are}\:\mathrm{parallel}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{and}\:\mathrm{t}\: \\ $$

Question Number 95773 Answers: 4 Comments: 0

Question Number 95772 Answers: 0 Comments: 3

Question Number 95770 Answers: 0 Comments: 8

the app doesn′t work properly for me any more. I open it and most of the time the home screen doesn′t show the forum. refreshing or trying to switch to the forum ends up in an endless turning loop...

$$\mathrm{the}\:\mathrm{app}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{work}\:\mathrm{properly}\:\mathrm{for}\:\mathrm{me}\:\mathrm{any} \\ $$$$\mathrm{more}.\:\mathrm{I}\:\mathrm{open}\:\mathrm{it}\:\mathrm{and}\:\mathrm{most}\:\mathrm{of}\:\mathrm{the}\:\mathrm{time}\:\mathrm{the} \\ $$$$\mathrm{home}\:\mathrm{screen}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{show}\:\mathrm{the}\:\mathrm{forum}. \\ $$$$\mathrm{refreshing}\:\mathrm{or}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{switch}\:\mathrm{to}\:\mathrm{the}\:\mathrm{forum} \\ $$$$\mathrm{ends}\:\mathrm{up}\:\mathrm{in}\:\mathrm{an}\:\mathrm{endless}\:\mathrm{turning}\:\mathrm{loop}... \\ $$

Question Number 95768 Answers: 0 Comments: 1

find x such that x≡3 (mod5) x≡5 (mod7) x≡7(mod11)

$$\mathrm{find}\:\mathrm{x}\:\mathrm{such}\:\mathrm{that}\: \\ $$$${x}\equiv\mathrm{3}\:\left(\mathrm{mod5}\right) \\ $$$${x}\equiv\mathrm{5}\:\left(\mathrm{mod7}\right) \\ $$$${x}\equiv\mathrm{7}\left(\mathrm{mod11}\right) \\ $$

Question Number 95767 Answers: 1 Comments: 0

Question Number 95766 Answers: 0 Comments: 1

Solve the equation 2^(2x) − 5x^2 + 4 = 0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{2x}} \:\:−\:\:\mathrm{5x}^{\mathrm{2}} \:\:+\:\:\mathrm{4}\:\:\:=\:\:\:\mathrm{0} \\ $$

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