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Question Number 29833    Answers: 1   Comments: 0

find cos^4 ((π/8)) +cos^4 (((3π)/8)) +cos^4 (((5π)/8)) +cos^4 (((7π)/8)).

$${find}\:\:{cos}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)\:+{cos}^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right). \\ $$

Question Number 29832    Answers: 0   Comments: 0

p is a polynomial having n roots x_i with x_i ≠x_j for i≠j prove that Σ_(i=1) ^n ((p^(′′) (x_i ))/(p^′ (x_i )))=0

$${p}\:{is}\:{a}\:{polynomial}\:{having}\:{n}\:{roots}\:{x}_{{i}} \:\:{with}\:{x}_{{i}} \neq{x}_{{j}} \:{for}\:{i}\neq{j} \\ $$$${prove}\:{that}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\:\frac{{p}^{''} \left({x}_{{i}} \right)}{{p}^{'} \left({x}_{{i}} \right)}=\mathrm{0} \\ $$

Question Number 29821    Answers: 1   Comments: 3

((sin 16x)/(sin x)) ?pls help.

$$\frac{\mathrm{sin}\:\mathrm{16x}}{\mathrm{sin}\:\mathrm{x}}\:\:\:\:\:\:?\mathrm{pls}\:\mathrm{help}. \\ $$

Question Number 29820    Answers: 1   Comments: 3

Question Number 29805    Answers: 0   Comments: 1

f(x)=(x+a_1 )(x+a_2 )(x+a_3 )...(x+a_n ) find the coefficient of term x^k (0≤k≤n)

$${f}\left({x}\right)=\left({x}+{a}_{\mathrm{1}} \right)\left({x}+{a}_{\mathrm{2}} \right)\left({x}+{a}_{\mathrm{3}} \right)...\left({x}+{a}_{{n}} \right) \\ $$$${find}\:{the}\:{coefficient}\:{of}\:{term}\:{x}^{{k}} \:\left(\mathrm{0}\leqslant{k}\leqslant{n}\right) \\ $$

Question Number 29818    Answers: 1   Comments: 0

4, 8, 16, 31, 57, 99, 163, T_8 ,T_9 , .... Find T_8 , T_9 .

$$\mathrm{4},\:\mathrm{8},\:\mathrm{16},\:\mathrm{31},\:\mathrm{57},\:\mathrm{99},\:\mathrm{163},\:{T}_{\mathrm{8}} \:,{T}_{\mathrm{9}} \:,\:.... \\ $$$${Find}\:{T}_{\mathrm{8}} \:,\:{T}_{\mathrm{9}} \:. \\ $$

Question Number 29794    Answers: 0   Comments: 9

Fluids:

$${Fluids}: \\ $$

Question Number 29831    Answers: 0   Comments: 0

let give f(x)= (1/(1+x^2 )) 1)prove that prove that f^((n)) (x)=((p_n (x))/((1+x^2 )^(n+1) )) with p_n is a polynomial 2) prove that p_(n+1) (x)=(1+x^2 )p_n ^′ (x) −2(n+1)p_n (x) 3) calculate p_0 (x) ,p_1 (x) ,p_2 (x) ,p_3 (x) .

$$\left.{let}\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\right){prove}\:{that}\:\:\:{prove}\:{that} \\ $$$${f}^{\left({n}\right)} \left({x}\right)=\frac{{p}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }\:{with}\:{p}_{{n}} {is}\:{a}\:{polynomial} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:{p}_{{n}+\mathrm{1}} \left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right){p}_{{n}} ^{'} \left({x}\right)\:−\mathrm{2}\left({n}+\mathrm{1}\right){p}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{p}_{\mathrm{0}} \left({x}\right)\:,{p}_{\mathrm{1}} \left({x}\right)\:,{p}_{\mathrm{2}} \left({x}\right)\:\:,{p}_{\mathrm{3}} \left({x}\right)\:\:. \\ $$

Question Number 29786    Answers: 0   Comments: 0

Question Number 29785    Answers: 0   Comments: 0

Question Number 29778    Answers: 1   Comments: 0

Question Number 29803    Answers: 0   Comments: 3

Question Number 29773    Answers: 0   Comments: 0

lim_(x→0,y→∞) xy=?

$$\underset{\mathrm{x}\rightarrow\mathrm{0},\mathrm{y}\rightarrow\infty} {\mathrm{lim}xy}=? \\ $$

Question Number 29753    Answers: 0   Comments: 0

$$ \\ $$

Question Number 29752    Answers: 0   Comments: 0

pls elp with dis... ∫(((1−x)dx)/((1+x)(√(1+x^2 +x^3 ))))

$$\mathrm{pls}\:\mathrm{elp}\:\mathrm{with}\:\mathrm{dis}... \\ $$$$ \\ $$$$\int\frac{\left(\mathrm{1}−\mathrm{x}\right)\boldsymbol{{dx}}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} }} \\ $$

Question Number 29770    Answers: 2   Comments: 0

find the equation of a pair of straight lines represented by given equation 2x^(2 ) −5xy−3y^2 +3x+19y−20=0

$${find}\:{the}\:{equation}\:{of}\:{a}\:{pair}\:{of}\:{straight}\:{lines}\:{represented}\:{by}\:{given}\:{equation}\:\mathrm{2}{x}^{\mathrm{2}\:} −\mathrm{5}{xy}−\mathrm{3}{y}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{19}{y}−\mathrm{20}=\mathrm{0} \\ $$

Question Number 29728    Answers: 0   Comments: 8

Question Number 29727    Answers: 1   Comments: 4

Question Number 29776    Answers: 0   Comments: 0

Question Number 29777    Answers: 2   Comments: 5

f(x) = (x − 1)(x − 2)(x − 3)...(x − 50) Find coefficient of x^(49)

$${f}\left({x}\right)\:=\:\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right)...\left({x}\:−\:\mathrm{50}\right) \\ $$$$\mathrm{Find}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{49}} \\ $$

Question Number 29726    Answers: 0   Comments: 2

Question Number 29887    Answers: 1   Comments: 3

Question Number 29723    Answers: 1   Comments: 1

Question Number 29700    Answers: 1   Comments: 0

32^(32^(32) ) /7...find remainder

$$\mathrm{32}^{\mathrm{32}^{\mathrm{32}} } \:/\mathrm{7}...\mathrm{find}\:\mathrm{remainder} \\ $$

Question Number 29689    Answers: 1   Comments: 2

find lim_(x→0) ((2/(1+a^x )))^(1/x) =?

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$

Question Number 29680    Answers: 1   Comments: 0

i^(i ) what is iota to power iota

$$\mathrm{i}^{\mathrm{i}\:} \:\:\mathrm{what}\:\mathrm{is}\:\mathrm{iota}\:\mathrm{to}\:\mathrm{power}\:\mathrm{iota} \\ $$

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