Question and Answers Forum

AllQuestion and Answers: Page 1029

Question Number 117250 Answers: 1 Comments: 0

calculate lim_(x→0) ((sin(xsh(2x))−sh(x sin(2x)))/x^3 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sin}\left(\mathrm{xsh}\left(\mathrm{2x}\right)\right)−\mathrm{sh}\left(\mathrm{x}\:\mathrm{sin}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 117249 Answers: 1 Comments: 0

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

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

Question Number 117243 Answers: 1 Comments: 1

Question Number 117228 Answers: 1 Comments: 0

(((x+y)/(y−1))) dx −(1/2)(((x+1)/(y−1)))^2 dy = 0

$$\left(\frac{{x}+{y}}{{y}−\mathrm{1}}\right)\:{dx}\:−\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{x}+\mathrm{1}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} {dy}\:=\:\mathrm{0} \\ $$

Question Number 117227 Answers: 0 Comments: 0

why every function that is Riemann integrable is not lebsgue integrable?

$${why}\:{every}\:{function}\:{that}\:{is}\:{Riemann} \\ $$$${integrable}\:{is}\:{not}\:{lebsgue}\:{integrable}? \\ $$

Question Number 117223 Answers: 1 Comments: 0

... nice mathematics... proof :: Ω = (1/π)∫_(0 ) ^( ∞) [tan^(−1) ((1/x))]^2 dx=ln(2) ... m.n.1970...

$$\:\:\:\:\:\:\:\:\:...\:{nice}\:\:{mathematics}... \\ $$$$\:\:{proof}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}\:} ^{\:\infty} \left[{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\right]^{\mathrm{2}} {dx}={ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:...\:\:{m}.{n}.\mathrm{1970}... \\ $$

Question Number 117221 Answers: 3 Comments: 1

∫_(−∞) ^( ∞) ((cos (3x))/(x^2 +4)) dx =?

$$\underset{−\infty} {\overset{\:\:\:\:\:\infty} {\int}}\:\frac{\mathrm{cos}\:\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}\:{dx}\:=? \\ $$

Question Number 117295 Answers: 1 Comments: 0

Question Number 117207 Answers: 0 Comments: 2

Can anyone recommend a pdf for learning hypergeometric functions?

$$\boldsymbol{\mathrm{C}}\mathrm{an}\:\mathrm{anyone}\:\mathrm{recommend}\:\mathrm{a}\:\mathrm{pdf}\:\mathrm{for} \\ $$$$\mathrm{learning}\:\mathrm{hypergeometric}\:\mathrm{functions}? \\ $$

Question Number 117286 Answers: 2 Comments: 0

A person wants to invite his 6 friends in a Dinner party. He has 3 person to send letter to them.In how many ways he can invite his 6 friends?

$${A}\:{person}\:{wants}\:{to}\:{invite}\:{his}\:\mathrm{6}\:{friends}\:{in}\:{a}\:{Dinner}\:{party}. \\ $$$${He}\:{has}\:\mathrm{3}\:{person}\:{to}\:{send}\:{letter}\:{to}\:{them}.{In}\:{how}\:{many}\:{ways} \\ $$$${he}\:{can}\:{invite}\:{his}\:\mathrm{6}\:{friends}? \\ $$

Question Number 117205 Answers: 0 Comments: 0

∫_0 ^( 2π) ((cos^2 3x)/(1−2a∙cosx+a^2 ))dx − ? (a∈C/{−1; 1}) I need a solution through complex analysis

$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\boldsymbol{{cos}}^{\mathrm{2}} \mathrm{3}\boldsymbol{{x}}}{\mathrm{1}−\mathrm{2}\boldsymbol{{a}}\centerdot\boldsymbol{{cosx}}+\boldsymbol{{a}}^{\mathrm{2}} }\boldsymbol{{dx}}\:−\:?\:\left(\boldsymbol{{a}}\in\boldsymbol{{C}}/\left\{−\mathrm{1};\:\mathrm{1}\right\}\right) \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{a}}\:\boldsymbol{{solution}}\:\boldsymbol{{through}}\:\boldsymbol{{complex}}\:\boldsymbol{{analysis}} \\ $$

Question Number 117204 Answers: 1 Comments: 2

Question Number 117215 Answers: 0 Comments: 1

v2.220: Forum viewing improvement • After update you will see options to zoom out of post with longer lines to view whole posts without scrolling. Similar option are added while editing in ′Cursor&Page′ menu

$$\mathrm{v2}.\mathrm{220}:\:\mathrm{Forum}\:\mathrm{viewing}\:\mathrm{improvement} \\ $$$$\bullet\:\mathrm{After}\:\mathrm{update}\:\mathrm{you}\:\mathrm{will}\:\mathrm{see}\:\mathrm{options} \\ $$$$\mathrm{to}\:\mathrm{zoom}\:\mathrm{out}\:\mathrm{of}\:\mathrm{post}\:\mathrm{with}\:\mathrm{longer}\:\mathrm{lines} \\ $$$$\mathrm{to}\:\mathrm{view}\:\mathrm{whole}\:\mathrm{posts}\:\mathrm{without}\:\mathrm{scrolling}. \\ $$$$\mathrm{Similar}\:\mathrm{option}\:\mathrm{are}\:\mathrm{added}\:\mathrm{while} \\ $$$$\mathrm{editing}\:\mathrm{in}\:'\mathrm{Cursor\&Page}'\:\mathrm{menu} \\ $$

Question Number 117192 Answers: 1 Comments: 0

Assuming you have enough coins of 1,5,10,25,and 50cents. In how many ways can you make a change for 1dollar.

$$\mathrm{Assuming}\:\mathrm{you}\:\mathrm{have}\:\mathrm{enough}\:\mathrm{coins}\: \\ $$$$\mathrm{of}\:\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{and}\:\mathrm{50cents}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{you}\:\mathrm{make}\:\mathrm{a}\:\mathrm{change}\:\mathrm{for}\:\mathrm{1dollar}. \\ $$

Question Number 117191 Answers: 0 Comments: 0

∫sin^(3/2) (x)dx

$$\int\mathrm{sin}^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 117188 Answers: 2 Comments: 1

Given r+(1/r) = (√2) , then r^8 +(1/r^8 ) = ?

$${Given}\:{r}+\frac{\mathrm{1}}{{r}}\:=\:\sqrt{\mathrm{2}}\:,\:{then}\:{r}^{\mathrm{8}} +\frac{\mathrm{1}}{{r}^{\mathrm{8}} }\:=\:?\: \\ $$

Question Number 117176 Answers: 4 Comments: 1

∫_(π/4) ^(π/2) ((4cot x+1 )/(4−cot x)) dx =?

$$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{4cot}\:{x}+\mathrm{1}\:}{\mathrm{4}−\mathrm{cot}\:{x}}\:{dx}\:=? \\ $$

Question Number 117172 Answers: 1 Comments: 0

Question Number 117171 Answers: 1 Comments: 0

lim_(x→0) (((1+x tan^(−1) (x))/(cosh (x))))^(1/(tan^2 (x))) =?

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

Question Number 117164 Answers: 2 Comments: 0

lim_(n→∞) (((n+9)/(2n−1)))^n =?

$$\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}+\mathrm{9}}{\mathrm{2n}−\mathrm{1}}\right)^{\mathrm{n}} =? \\ $$

Question Number 117163 Answers: 2 Comments: 0

∫ ((4 dx)/(x (√(x^2 −1)))) =?

$$\:\:\:\int\:\frac{\mathrm{4}\:\mathrm{dx}}{\mathrm{x}\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:=? \\ $$

Question Number 117144 Answers: 1 Comments: 0

S_n =Π_(k=1) ^n cos(kx)=?????? please help

$$\boldsymbol{{S}}_{\boldsymbol{{n}}} =\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\prod}}\boldsymbol{{cos}}\left(\boldsymbol{{kx}}\right)=?????? \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}} \\ $$

Question Number 117143 Answers: 1 Comments: 0

Question Number 117142 Answers: 0 Comments: 0

Question Number 117140 Answers: 1 Comments: 0

Question Number 117216 Answers: 1 Comments: 0

∫_0 ^(π/2) (dx/( (√(sin x)))) =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{dx}}{\:\sqrt{\mathrm{sin}\:\mathrm{x}}}\:=?\: \\ $$$$ \\ $$

Pg 1024 Pg 1025 Pg 1026 Pg 1027 Pg 1028 Pg 1029 Pg 1030 Pg 1031 Pg 1032 Pg 1033

Contact: [email protected]