Question and Answers Forum

AllQuestion and Answers: Page 1142

Question Number 95592 Answers: 0 Comments: 1

∫ ((sin 2x)/(sin^4 x + cos^4 x)) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:\mathrm{dx} \\ $$

Question Number 95473 Answers: 1 Comments: 0

Question Number 95471 Answers: 0 Comments: 1

(y^2 −6y) how factorise this one?

$$\left(\mathrm{y}^{\mathrm{2}} −\mathrm{6y}\right) \\ $$$$\mathrm{how}\:\mathrm{factorise}\:\mathrm{this}\:\mathrm{one}? \\ $$

Question Number 95469 Answers: 0 Comments: 1

(9b^2 −25) why is this inside the bracket as it is a diffetence of two squares?

$$\left(\mathrm{9b}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$$\mathrm{why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{bracket}\:\mathrm{as}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diffetence}\:\mathrm{of}\:\mathrm{two}\:\mathrm{squares}? \\ $$

Question Number 95465 Answers: 1 Comments: 0

solve y^(′′) −y^′ +2 =x^2 e^(−x) with y(0) =1 and y^′ (0) =−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{2}\:\:\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}} \:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$

Question Number 95464 Answers: 0 Comments: 8

Question Number 95456 Answers: 0 Comments: 0

solve on R y′+xy=y^2 +1 y(0)=a ∈R

$${solve}\:{on}\:\mathbb{R}\: \\ $$$$\:\:{y}'+{xy}={y}^{\mathrm{2}} +\mathrm{1}\:\:\:\:\:\:\:\:{y}\left(\mathrm{0}\right)={a}\:\in\mathbb{R} \\ $$

Question Number 95449 Answers: 1 Comments: 7

∫∫ (√(x^2 +y^2 )) dxdy = where D : x^2 +y^2 ≤ 100

$$\int\int\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\mathrm{dxdy}\:=\: \\ $$$$\mathrm{where}\:\mathrm{D}\::\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\leqslant\:\mathrm{100}\: \\ $$

Question Number 95447 Answers: 1 Comments: 0

can I write the solution of ay′′+by′+cy=0 y= { ((c_1 e^(((−b+(√(b^2 −4ac)))/2)x) +c_2 e^(((−b−(√(b^2 −4ac)))/2)x) ,when b^2 −4ac≠0)),((c_1 e^(((−b)/2)x) +c_2 xe^(((−b)/2)x) ,when b^2 −4ac=0)) :} in one sentence not in the form of piecewide-define function

$${can}\:{I}\:{write}\:{the}\:{solution}\:{of} \\ $$$${ay}''+{by}'+{cy}=\mathrm{0} \\ $$$${y}=\begin{cases}{{c}_{\mathrm{1}} {e}^{\frac{−{b}+\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {e}^{\frac{−{b}−\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} ,{when}\:{b}^{\mathrm{2}} −\mathrm{4}{ac}\neq\mathrm{0}}\\{{c}_{\mathrm{1}} {e}^{\frac{−{b}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {xe}^{\frac{−{b}}{\mathrm{2}}{x}} ,{when}\:{b}^{\mathrm{2}} −\mathrm{4}{ac}=\mathrm{0}}\end{cases} \\ $$$${in}\:{one}\:{sentence} \\ $$$${not}\:{in}\:{the}\:{form}\:{of}\:{piecewide}-{define}\:{function} \\ $$

Question Number 95440 Answers: 1 Comments: 0

Question Number 95436 Answers: 1 Comments: 0

∫((x^4 dx)/(x^8 +x^4 +1))

$$\int\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\mathrm{x}^{\mathrm{8}} +\mathrm{x}^{\mathrm{4}} +\mathrm{1}} \\ $$

Question Number 95424 Answers: 2 Comments: 1

without calculator tan^2 36^o × tan^2 72^o ?

$$\mathrm{without}\:\mathrm{calculator}\: \\ $$$$\mathrm{tan}\:^{\mathrm{2}} \mathrm{36}^{\mathrm{o}} \:×\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{72}^{\mathrm{o}} \:? \\ $$

Question Number 95420 Answers: 0 Comments: 7

tinkutara admint I want to update to version 2.074

$$\mathrm{tinkutara}\:\mathrm{admint} \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{update}\:\mathrm{to}\:\mathrm{version}\:\mathrm{2}.\mathrm{074} \\ $$

Question Number 95417 Answers: 1 Comments: 0

find the solution of eq 3cot 2x + 2sin x = 0 for x∈[0,360^o ]

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{eq}\: \\ $$$$\mathrm{3cot}\:\mathrm{2x}\:+\:\mathrm{2sin}\:\mathrm{x}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{360}^{\mathrm{o}} \right] \\ $$

Question Number 95416 Answers: 1 Comments: 4

It takes 12 hours to fill a swimming pool using 2 pipes. If the larger pipe used , for 4 hours and the small pipe for 9 hours, only half the pool is filled. How long would it take for each pipe alone to fill the pool?

$$\mathrm{It}\:\mathrm{takes}\:\mathrm{12}\:\mathrm{hours}\:\mathrm{to}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{swimming}\: \\ $$$$\mathrm{pool}\:\mathrm{using}\:\mathrm{2}\:\mathrm{pipes}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{larger}\: \\ $$$$\mathrm{pipe}\:\mathrm{used}\:,\:\mathrm{for}\:\mathrm{4}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{small}\:\mathrm{pipe}\:\mathrm{for}\:\mathrm{9}\:\mathrm{hours},\:\mathrm{only}\:\mathrm{half} \\ $$$$\mathrm{the}\:\mathrm{pool}\:\mathrm{is}\:\mathrm{filled}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\: \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{each}\:\mathrm{pipe}\:\mathrm{alone}\:\mathrm{to}\: \\ $$$$\mathrm{fill}\:\mathrm{the}\:\mathrm{pool}? \\ $$

Question Number 95405 Answers: 1 Comments: 3

∫ e^x (tan x−ln(cos x)) dx ?

$$\int\:\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{tan}\:\mathrm{x}−\mathrm{ln}\left(\mathrm{cos}\:\mathrm{x}\right)\right)\:\mathrm{dx}\:? \\ $$

Question Number 95401 Answers: 2 Comments: 0

lim_(n→∞) n^(3/2) {(√(n+1))+(√(n−1))−2(√n) }

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}^{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\sqrt{\mathrm{n}+\mathrm{1}}+\sqrt{\mathrm{n}−\mathrm{1}}−\mathrm{2}\sqrt{\mathrm{n}}\:\right\}\: \\ $$

Question Number 95397 Answers: 0 Comments: 2

f(x)=(1/(lnx)) −(1/(x−1)) 1) lim_(x→1) f(x)=(1/2) 2) ∫_0 ^1 f(x)dx= γ

$${f}\left({x}\right)=\frac{\mathrm{1}}{{lnx}}\:−\frac{\mathrm{1}}{{x}−\mathrm{1}}\: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}=\:\gamma\: \\ $$

Question Number 95396 Answers: 0 Comments: 2

∫_0 ^∞ e^(−x^2 −(1/x^2 )) dx = ((√π)/(2e^2 ))