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Question Number 72397    Answers: 0   Comments: 4

find A(x)=∫_0 ^(π/2) ln(1−xsin^2 θ)dθ with ∣x∣<1

$${find}\:{A}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{xsin}^{\mathrm{2}} \theta\right){d}\theta\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 72396    Answers: 0   Comments: 2

calculate ∫_0 ^∞ ((1+x^2 )/(2+x^2 +x^4 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 72395    Answers: 0   Comments: 0

find Σ_(k=0) ^n (C_n ^k )^3

$${find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \left({C}_{{n}} ^{{k}} \right)^{\mathrm{3}} \\ $$

Question Number 72394    Answers: 0   Comments: 3

let g(x)=((ln(1+x))/(3+x^2 )) 1) find g^((n)) (x)and g^((n)) (0) 2)developp g at integr serie

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

Question Number 72393    Answers: 0   Comments: 0

let f(x) =cos(narccosx) 1)calculate f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie

$${let}\:{f}\left({x}\right)\:={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 72392    Answers: 0   Comments: 1

calculate A_n =∫_0 ^∞ e^(−nx) ln(1+x)dx with n natural ≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} {ln}\left(\mathrm{1}+{x}\right){dx}\:\:{with}\:{n}\:{natural}\:\geqslant\mathrm{1} \\ $$

Question Number 72391    Answers: 0   Comments: 1

calculte ∫_0 ^∞ (((−1)^([x]) )/(4+x^2 ))dx

$${calculte}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 72362    Answers: 1   Comments: 0

Calculate the sides of a triangle knowing the heights h_(a ) =(1/9) h_b =(1/7) and h_c =(1/4)

$${Calculate}\:{the}\:{sides}\:{of}\:{a}\:{triangle} \\ $$$${knowing}\:{the}\:{heights}\:{h}_{\mathrm{a}\:} =\frac{\mathrm{1}}{\mathrm{9}} \\ $$$${h}_{\mathrm{b}} =\frac{\mathrm{1}}{\mathrm{7}}\:{and}\:{h}_{\mathrm{c}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 72462    Answers: 0   Comments: 2

lim_(x→0) ((1−(√(1+4x ))cos(x^2 ))/(x^3 arctan(x^5 )))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{4x}\:}\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \mathrm{arctan}\left(\mathrm{x}^{\mathrm{5}} \right)} \\ $$

Question Number 72346    Answers: 0   Comments: 1

Question Number 72344    Answers: 0   Comments: 3

prove that e^(lnx) = x or a^(log_a x) = x

$${prove}\:{that}\:\:{e}^{{lnx}} \:=\:{x} \\ $$$${or}\:\:{a}^{{log}_{{a}} {x}} \:=\:{x} \\ $$

Question Number 72343    Answers: 0   Comments: 3

given that y = ln ( 1 + cos^2 x) find (dy/(dx )) at the point x = ((3π)/4) and if y =ln(x^2 + 4) find (dy/dx) at x = 1

$${given}\:{that}\:{y}\:=\:{ln}\:\left(\:\mathrm{1}\:+\:{cos}^{\mathrm{2}} {x}\right)\:{find}\:\frac{{dy}}{{dx}\:\:}\:{at}\:{the}\:{point}\:\:{x}\:=\:\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$$${and}\:\:{if}\:\:{y}\:={ln}\left({x}^{\mathrm{2}} \:+\:\mathrm{4}\right)\:{find}\:\:\frac{{dy}}{{dx}}\:{at}\:{x}\:=\:\mathrm{1} \\ $$

Question Number 72339    Answers: 0   Comments: 1

(√(x + (√(4x + (√(16x + ... + (√(4^(2019) x + 3)))))))) = (√x) + 1

$$\sqrt{{x}\:+\:\sqrt{\mathrm{4}{x}\:+\:\sqrt{\mathrm{16}{x}\:+\:...\:+\:\sqrt{\mathrm{4}^{\mathrm{2019}} {x}\:+\:\mathrm{3}}}}}\:\:=\:\:\sqrt{{x}}\:+\:\mathrm{1} \\ $$

Question Number 72337    Answers: 1   Comments: 1

Evaluate ∫_(−5) ^5 ((√(25−x^2 )) ) dx using ⇒ an algebraic method ⇒ Geometrical mehod thanks in advanced great mathematicians

$${Evaluate}\:\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\:\right)\:{dx}\:{using} \\ $$$$\Rightarrow\:{an}\:{algebraic}\:{method} \\ $$$$\Rightarrow\:{Geometrical}\:{mehod}\: \\ $$$${thanks}\:{in}\:{advanced}\:{great}\:{mathematicians} \\ $$

Question Number 72336    Answers: 0   Comments: 0

Obain an equation for ⇒ the left Reimen Sum ⇒ the right Reimen sum ⇒ Trapeziodal rule ⇒ Newton Raphson′s Iteration Hence find and approximate value for ∫_0 ^3 (e^x + x^2 )dx

$${Obain}\:{an}\:{equation}\:{for}\: \\ $$$$\Rightarrow\:{the}\:{left}\:{Reimen}\:{Sum} \\ $$$$\Rightarrow\:{the}\:{right}\:{Reimen}\:{sum} \\ $$$$\Rightarrow\:{Trapeziodal}\:{rule} \\ $$$$\Rightarrow\:{Newton}\:{Raphson}'{s}\:{Iteration} \\ $$$$\:\:{Hence}\:{find}\:{and}\:{approximate}\:{value}\:{for}\:\int_{\mathrm{0}} ^{\mathrm{3}} \left({e}^{{x}} \:+\:{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 72332    Answers: 1   Comments: 0

let Q=((1+tan(((3π)/8)) . tan((π/(10))))/(1−tan((π/8)).tan((π/(10))))) prove that ((Q−1)/(Q+1))=(√(7−3(√5)−(√(85−38(√5)))))

$${let}\:{Q}=\frac{\mathrm{1}+{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:.\:{tan}\left(\frac{\pi}{\mathrm{10}}\right)}{\mathrm{1}−{tan}\left(\frac{\pi}{\mathrm{8}}\right).{tan}\left(\frac{\pi}{\mathrm{10}}\right)} \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$\: \\ $$$$\frac{{Q}−\mathrm{1}}{{Q}+\mathrm{1}}=\sqrt{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}−\sqrt{\mathrm{85}−\mathrm{38}\sqrt{\mathrm{5}}}} \\ $$$$ \\ $$

Question Number 72316    Answers: 0   Comments: 6

To whom it may concern! To solve some of your questions, I spent a lot of my time and gave much effort to prepare some diagrams. I did′t keep any backup for my answers and especially for the diagrams in my own device, because I thought they were saved in the forum. Since you, I don′t understand why, have deleted these answered questions, I also lose my answers and my diagrams forever. You don′t need to say a “thank you” for the help I give you, but you should be at least polite and respect me and my work. As far as I think you are such a person, regardless how you change your ID, I won′t answer any of your questions even when I know the answer. NOBODY HAS THE RIGHT TO DELETE MY ANSWERS. THEY ARE GIVEN TO ALL MEMBERS OF THE FORUM, NOT FOR YOU PERSONALLY!

$$\boldsymbol{\mathrm{T}{o}}\:\boldsymbol{{whom}}\:\boldsymbol{{it}}\:\boldsymbol{{may}}\:\boldsymbol{{concern}}! \\ $$$${To}\:{solve}\:{some}\:{of}\:{your}\:{questions},\:{I}\: \\ $$$${spent}\:{a}\:{lot}\:{of}\:{my}\:{time}\:{and}\:{gave}\:{much} \\ $$$${effort}\:{to}\:{prepare}\:{some}\:{diagrams}.\:{I} \\ $$$${did}'{t}\:{keep}\:{any}\:{backup}\:{for}\:{my}\:{answers} \\ $$$${and}\:{especially}\:{for}\:{the}\:{diagrams}\:{in}\:{my} \\ $$$${own}\:{device},\:{because}\:{I}\:{thought}\:{they}\: \\ $$$${were}\:{saved}\:{in}\:{the}\:{forum}.\:{Since}\:{you}, \\ $$$${I}\:{don}'{t}\:{understand}\:{why},\:{have}\:{deleted} \\ $$$${these}\:{answered}\:{questions},\:{I}\:{also}\:{lose} \\ $$$${my}\:{answers}\:{and}\:{my}\:{diagrams}\:{forever}. \\ $$$$ \\ $$$${You}\:{don}'{t}\:{need}\:{to}\:{say}\:{a}\:``{thank}\:{you}''\:{for} \\ $$$${the}\:{help}\:{I}\:{give}\:{you},\:{but}\:{you}\:{should}\:{be} \\ $$$${at}\:{least}\:{polite}\:{and}\:{respect}\:{me}\:{and}\:{my} \\ $$$${work}. \\ $$$$ \\ $$$${As}\:{far}\:{as}\:{I}\:{think}\:{you}\:{are}\:{such}\:{a}\:{person}, \\ $$$${regardless}\:{how}\:{you}\:{change}\:{your}\:{ID}, \\ $$$${I}\:{won}'{t}\:{answer}\:{any}\:{of}\:{your}\:{questions} \\ $$$${even}\:{when}\:{I}\:{know}\:{the}\:{answer}. \\ $$$$ \\ $$$${NOBODY}\:{HAS}\:{THE}\:{RIGHT}\:{TO} \\ $$$${DELETE}\:{MY}\:{ANSWERS}.\:{THEY} \\ $$$${ARE}\:{GIVEN}\:{TO}\:{ALL}\:{MEMBERS}\:{OF} \\ $$$${THE}\:{FORUM},\:{NOT}\:{FOR}\:{YOU} \\ $$$${PERSONALLY}! \\ $$

Question Number 72359    Answers: 1   Comments: 2

Question Number 72296    Answers: 1   Comments: 4

Let x = f(x) e^(f(x)) ∫_( 0) ^( e) f(x) dx = ?

$${Let}\:\:\:\:{x}\:\:=\:\:{f}\left({x}\right)\:{e}^{{f}\left({x}\right)} \\ $$$$\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}\overset{\:{e}} {\:}{f}\left({x}\right)\:{dx}\:\:=\:\:? \\ $$

Question Number 72294    Answers: 1   Comments: 4

Question Number 72291    Answers: 1   Comments: 0

Question Number 72289    Answers: 2   Comments: 0

Bonjour. Aidez moi a resoudre le systeme suivant dans R^2 x−y=2 xy=20

$${Bonjour}. \\ $$$${Aidez}\:{moi}\:{a}\:{resoudre}\:{le}\:{systeme}\: \\ $$$${suivant}\:\:\:\:{dans}\:\mathbb{R}^{\mathrm{2}} \:\:\:\:\: \\ $$$${x}−{y}=\mathrm{2} \\ $$$${xy}=\mathrm{20} \\ $$

Question Number 72275    Answers: 0   Comments: 2

Σ_(i=1) ^6 X_i =42 Find X_1 and X_3

$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{X}_{{i}} =\mathrm{42} \\ $$$${Find}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{3}} \\ $$

Question Number 72260    Answers: 1   Comments: 3

let f(x)=((2x+3)/(x^2 +1)) calculate f^((n)) (x) 2)find f^((10)) (x) and f^((15)) (x) 3)calculate f^((10)) (0) and f^((15)) (0) 4)developp f at integr serie 5)let g(x)=∫_0 ^x f(t)dt developp g at integr serie.

$${let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${calculate}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{f}^{\left(\mathrm{10}\right)} \left({x}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left({x}\right) \\ $$$$\left.\mathrm{3}\right){calculate}\:{f}^{\left(\mathrm{10}\right)} \left(\mathrm{0}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{4}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{5}\right){let}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {f}\left({t}\right){dt}\:\:{developp}\:{g}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 72259    Answers: 1   Comments: 0

∫yz dx +∫xz dy +∫xy dz pleas sir help me ?

$$\int{yz}\:{dx}\:+\int{xz}\:{dy}\:+\int{xy}\:{dz}\:\:\:\:{pleas}\:{sir}\:{help}\:{me}\:? \\ $$

Question Number 72286    Answers: 0   Comments: 0

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