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Question Number 75762 Answers: 0 Comments: 0

if y cos(x)+x cos(y) = π find (d^2 y/dx^2 ) , x=0

$${if}\:\:{y}\:{cos}\left({x}\right)+{x}\:{cos}\left({y}\right)\:=\:\pi \\ $$$$ \\ $$$${find}\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:\:\:,\:{x}=\mathrm{0} \\ $$

Question Number 75756 Answers: 0 Comments: 1

Σ_(x=1) ^(99) ((1/(2x+1)))

$$\underset{{x}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}\right) \\ $$

Question Number 75753 Answers: 1 Comments: 0

((((x^(1/3) +x^(−1/3) )^2 −2)/((x^(1/3) +x^(−1/3) )^2 +2))−x)^(3/4)

$$\left(\frac{\left(\mathrm{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{x}^{−\mathrm{1}/\mathrm{3}} \right)^{\mathrm{2}} −\mathrm{2}}{\left(\mathrm{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{x}^{−\mathrm{1}/\mathrm{3}} \right)^{\mathrm{2}} +\mathrm{2}}−\mathrm{x}\right)^{\mathrm{3}/\mathrm{4}} \\ $$

Question Number 75751 Answers: 0 Comments: 0

Question Number 75750 Answers: 0 Comments: 2

Question Number 75743 Answers: 2 Comments: 3

Question Number 75742 Answers: 0 Comments: 0

plz solve this my handsome guys and sisters... complex integral ∫_(−∞) ^(+∞) (e^(it) /(√(1+t^2 )))dt

$$\mathrm{plz}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{my}\:\mathrm{handsome}\:\mathrm{guys}\:\mathrm{and}\:\mathrm{sisters}... \\ $$$$\mathrm{complex}\:\mathrm{integral}\:\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t} \\ $$

Question Number 75741 Answers: 0 Comments: 0

solve complex integral ∫_(−∞) ^(+∞) (e^(it) /(√(1+t^2 )))dt=???? plz.......help me...T⌢T my handsome brothers and sisters...

$$\mathrm{solve}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t}=???? \\ $$$$\mathrm{plz}.......\mathrm{help}\:\mathrm{me}...\mathrm{T}\frown\mathrm{T}\:\:\: \\ $$$$\mathrm{my}\:\mathrm{handsome}\:\mathrm{brothers}\:\mathrm{and}\:\mathrm{sisters}... \\ $$

Question Number 75736 Answers: 0 Comments: 0

let A_n = ((((π/n) 1)),((−1 (π/n))) ) with n integr natural not0 1) find A_n ^n 2) calculate lim_(n→+∞) A_n ^n

$${let}\:{A}_{{n}} =\:\begin{pmatrix}{\frac{\pi}{{n}}\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\frac{\pi}{{n}}}\end{pmatrix}\:\:\:\:{with}\:{n}\:{integr}\:{natural}\:{not}\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} ^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} ^{{n}} \\ $$

Question Number 75735 Answers: 0 Comments: 4

let A = (((1 1)),((3 −1)) ) 1) calculate A^n 2) find e^A and e^(−A) 3) find cosA and sinA

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{cosA}\:{and}\:{sinA} \\ $$

Question Number 75734 Answers: 0 Comments: 0

calculate f(x)=∫_0 ^(π/4) ln(1+xtanθ)dθ with x >0

$${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{xtan}\theta\right){d}\theta\:\:{with}\:{x}\:>\mathrm{0} \\ $$

Question Number 75739 Answers: 1 Comments: 1

Question Number 75701 Answers: 2 Comments: 1

please tell me :(∞)^(0 ) is not defined ?

$$\mathrm{please}\:\mathrm{tell}\:\mathrm{me}\::\left(\infty\right)^{\mathrm{0}\:} \mathrm{is}\:\mathrm{not}\:\mathrm{defined}\:? \\ $$

Question Number 75694 Answers: 3 Comments: 0

prove that lim_(x→∞) x^(1/x) =1

$$\boldsymbol{{prove}}\:\boldsymbol{{that}}\: \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\boldsymbol{{x}}^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} \:=\mathrm{1} \\ $$

Question Number 75721 Answers: 0 Comments: 1

solve this complex integral∫_(−∞) ^(+∞) (e^(it) /(√(1+t^2 )))dt

$$\mathrm{solve}\:\mathrm{this}\:\mathrm{complex}\:\mathrm{integral}\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t} \\ $$

Question Number 75684 Answers: 2 Comments: 2

Question Number 75681 Answers: 1 Comments: 8

Question Number 75669 Answers: 3 Comments: 3

Question Number 75662 Answers: 0 Comments: 0

Question Number 75661 Answers: 1 Comments: 0

Question Number 75660 Answers: 2 Comments: 1

find all solutions (if exist) of x^2 +5y^2 =2016 with x,y ∈ N.

$${find}\:{all}\:{solutions}\:\left({if}\:{exist}\right)\:{of} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} =\mathrm{2016} \\ $$$${with}\:{x},{y}\:\in\:\mathbb{N}. \\ $$

Question Number 75656 Answers: 0 Comments: 5

Question Number 75655 Answers: 1 Comments: 0

if z ∈ C is sin^2 z+cos^2 z=1 also valid?

$${if}\:{z}\:\in\:\mathbb{C} \\ $$$${is}\:\mathrm{sin}^{\mathrm{2}} \:{z}+\mathrm{cos}^{\mathrm{2}} \:{z}=\mathrm{1}\:{also}\:{valid}? \\ $$

Question Number 75648 Answers: 0 Comments: 0

A student seals 200g of ice−cold water in a glass vacuum (thermos) flask and finds that it warms up by 3.5 K in one hour SHC of water =2400 Jkg^(−1) K^(−1) a) Calculate the average rate of heat flow in the flask in watts. To check this result over a longer period,the student fills the flask with equal amounts of ice and water all at 0°C, and leaves it for 4 hours. the specific latent heat(enthalpy) of fusion of ice is 0.33MJg^(−1) b) How much ice would you expect to have melted at the end of the four hours?

$$\:{A}\:{student}\:{seals}\:\mathrm{200}{g}\:{of}\:{ice}−{cold}\:{water}\:{in}\:{a}\:{glass}\:{vacuum} \\ $$$$\left({thermos}\right)\:{flask}\:{and}\:{finds}\:{that}\:{it}\:{warms}\:{up}\:{by}\:\mathrm{3}.\mathrm{5}\:{K}\:{in}\:{one}\:{hour} \\ $$$${SHC}\:{of}\:{water}\:=\mathrm{2400}\:{Jkg}^{−\mathrm{1}} {K}^{−\mathrm{1}} \\ $$$$\left.{a}\right)\:{Calculate}\:{the}\:{average}\:{rate}\:{of}\:{heat}\:{flow}\:{in}\:{the}\:{flask}\:{in}\:{watts}. \\ $$$${To}\:{check}\:{this}\:{result}\:{over}\:{a}\:{longer}\:{period},{the}\:{student}\:{fills}\:{the}\:{flask}\:{with} \\ $$$${equal}\:{amounts}\:{of}\:{ice}\:{and}\:{water}\:{all}\:{at}\:\mathrm{0}°{C},\:{and}\:{leaves}\:{it}\:{for}\: \\ $$$$\mathrm{4}\:{hours}.\:{the}\:{specific}\:{latent}\:{heat}\left({enthalpy}\right)\:{of}\:{fusion}\:{of}\:{ice}\:{is}\:\mathrm{0}.\mathrm{33}{MJg}^{−\mathrm{1}} \\ $$$$\left.{b}\right)\:{How}\:{much}\:{ice}\:{would}\:{you}\:{expect}\:{to}\:{have}\:{melted}\:{at}\:{the}\:{end}\:{of}\:{the} \\ $$$${four}\:{hours}? \\ $$

Question Number 75748 Answers: 0 Comments: 0

((4 sin (((2π)/7)) + sec ((π/(14))))/(cot ((π/7)))) = ?

$$\frac{\mathrm{4}\:\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\:+\:\mathrm{sec}\:\left(\frac{\pi}{\mathrm{14}}\right)}{\mathrm{cot}\:\left(\frac{\pi}{\mathrm{7}}\right)}\:=\:? \\ $$

Question Number 75641 Answers: 2 Comments: 1

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