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Question Number 161391 Answers: 0 Comments: 4

f^( 3) (x)+x^2 f(x)=2x^3 +4x^2 +3x+1 ∀x∈R

$$\:\:{f}^{\:\mathrm{3}} \left({x}\right)+{x}^{\mathrm{2}} \:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1} \\ $$$$\:\forall{x}\in\mathbb{R}\: \\ $$

Question Number 161387 Answers: 0 Comments: 0

sin(√(1+π^2 n^2 )) ∼ (((−1)^n )/(2πn)) ?

$$\:{sin}\sqrt{\mathrm{1}+\pi^{\mathrm{2}} {n}^{\mathrm{2}} }\:\sim\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}\pi{n}}\:\:? \\ $$

Question Number 161386 Answers: 0 Comments: 0

Question Number 161378 Answers: 0 Comments: 0

determine, pour tout α∈R, la nature de la serie de terme general U_n =Σ_(k=1) ^n (1/((k^2 +(n−k)^2 )^α )) besoin d′aide svp please help me

$${determine},\:{pour}\:{tout}\:\alpha\in\mathbb{R},\:\:{la}\:{nature} \\ $$$$\:{de}\:{la}\:{serie}\:{de}\:{terme}\:{general} \\ $$$${U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\left({k}^{\mathrm{2}} +\left({n}−{k}\right)^{\mathrm{2}} \right)^{\alpha} } \\ $$$${besoin}\:{d}'{aide}\:{svp} \\ $$$${please}\:{help}\:{me} \\ $$

Question Number 161377 Answers: 3 Comments: 2

please calculate A and B. A = (1 − (1/4))(1 − (1/9))(1 − (1/(16)))...(1 − (1/(4 084 441))) (and 2021^(2 ) = 4084441 ) B = (1^2 −2^2 −3^2 + 4^2 ) + ( 5^2 − 6^2 −7^2 +8^2 ) +(9^2 −10^2 −11^2 +12^2 )+... +(2021^2 −2022^2 −2023^2 +2024^(2 ) )

$${please}\:{calculate}\:{A}\:{and}\:\:{B}. \\ $$$$ \\ $$$${A}\:=\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{9}}\right)\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{16}}\right)...\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{4}\:\mathrm{084}\:\mathrm{441}}\right)\:\:\left({and}\:\mathrm{2021}^{\mathrm{2}\:} =\:\mathrm{4084441}\:\right) \\ $$$${B}\:=\:\left(\mathrm{1}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} \:−\mathrm{3}^{\mathrm{2}} \:+\:\mathrm{4}^{\mathrm{2}} \right)\:+\:\left(\:\mathrm{5}^{\mathrm{2}} \:−\:\mathrm{6}^{\mathrm{2}} \:−\mathrm{7}^{\mathrm{2}} \:+\mathrm{8}^{\mathrm{2}} \right)\:+\left(\mathrm{9}^{\mathrm{2}} \:−\mathrm{10}^{\mathrm{2}} \:−\mathrm{11}^{\mathrm{2}} \:+\mathrm{12}^{\mathrm{2}} \right)+...\:+\left(\mathrm{2021}^{\mathrm{2}} \:−\mathrm{2022}^{\mathrm{2}} \:−\mathrm{2023}^{\mathrm{2}} \:+\mathrm{2024}^{\mathrm{2}\:} \right) \\ $$

Question Number 161381 Answers: 1 Comments: 0

∫ (dy/( (√(ae^y +1))))

$$\int\:\frac{{dy}}{\:\sqrt{{ae}^{{y}} +\mathrm{1}}} \\ $$

Question Number 161371 Answers: 0 Comments: 0

1.The Trapejoidal Rule ∫_x_o ^(x_o +nh) ydx=(h/2)[(y_o +y_n )+2(y_1 +y_2 +y_3 ....]

$$\:\mathrm{1}.{The}\:{Trapejoidal}\:{Rule} \\ $$$$\int_{{x}_{{o}} } ^{{x}_{{o}} +{nh}} {ydx}=\frac{{h}}{\mathrm{2}}\left[\left({y}_{{o}} +{y}_{{n}} \right)+\mathrm{2}\left({y}_{\mathrm{1}} +{y}_{\mathrm{2}} +{y}_{\mathrm{3}} ....\right]\right. \\ $$

Question Number 161369 Answers: 2 Comments: 0

Determine the value of the following proposition . ( True or False ) ∃ x ∈ R ; determinant ((( 1+2x),( 2x),(2x)),(( 2x),( 1+2x),( 2x )),(( 2x),( 2x),(1 +2x)))= x^( 3) + 8x−2 −−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\mathrm{D}{etermine}\:{the}\:{value}\:{of}\:{the}\:{following} \\ $$$$\:\:\:\:\:\:\:{proposition}\:.\:\left(\:\:\mathrm{T}{rue}\:\:{or}\:\:\mathrm{F}{alse}\:\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\exists\:{x}\:\in\:\mathbb{R}\:;\:\:\begin{vmatrix}{\:\mathrm{1}+\mathrm{2}{x}}&{\:\mathrm{2}{x}}&{\mathrm{2}{x}}\\{\:\:\mathrm{2}{x}}&{\:\mathrm{1}+\mathrm{2}{x}}&{\:\mathrm{2}{x}\:}\\{\:\:\mathrm{2}{x}}&{\:\mathrm{2}{x}}&{\mathrm{1}\:+\mathrm{2}{x}}\end{vmatrix}=\:{x}^{\:\mathrm{3}} +\:\mathrm{8}{x}−\mathrm{2}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\ $$$$\:\:\: \\ $$

Question Number 161366 Answers: 2 Comments: 0

[similar question reposted] if a+(3/b)=b+(3/c)=c+(3/a) with a≠b≠c and a,b,c ∈ R. find (abc)^2 =?

Question Number 161362 Answers: 0 Comments: 1

log _(√(x/3)) (3x−54)^(log _3 (x)) = 18−3log _(x/3) (x^2 ) x=?

$$\:\mathrm{log}\:_{\sqrt{\frac{{x}}{\mathrm{3}}}} \left(\mathrm{3}{x}−\mathrm{54}\right)^{\mathrm{log}\:_{\mathrm{3}} \left({x}\right)} \:=\:\mathrm{18}−\mathrm{3log}\:_{\frac{{x}}{\mathrm{3}}} \left({x}^{\mathrm{2}} \right) \\ $$$$\:{x}=? \\ $$

Question Number 161361 Answers: 0 Comments: 1

lim_(x→0) (((√(x+1)) +((1+2x))^(1/h) −2)/x) = (3/5) h^3 −(2/9)(h+7)=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}\:+\sqrt[{{h}}]{\mathrm{1}+\mathrm{2}{x}}−\mathrm{2}}{{x}}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\: \\ $$$$\:\:{h}^{\mathrm{3}} −\frac{\mathrm{2}}{\mathrm{9}}\left({h}+\mathrm{7}\right)=? \\ $$

Question Number 161356 Answers: 1 Comments: 2

a + b + c = 0 Find the value of (((b−c)/a) + ((c−a)/b) + ((a−b)/c))((a/(b−c)) + (b/(c−a)) + (c/(a−b))) .

$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0} \\ $$$$ \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\left(\frac{{b}−{c}}{{a}}\:+\:\frac{{c}−{a}}{{b}}\:+\:\frac{{a}−{b}}{{c}}\right)\left(\frac{{a}}{{b}−{c}}\:+\:\frac{{b}}{{c}−{a}}\:+\:\frac{{c}}{{a}−{b}}\right)\:. \\ $$