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Question Number 77752 Answers: 0 Comments: 1

let f(λ) =∫_(−∞) ^(+∞) ((sin( λe^x +e^(−x) ))/(x^2 +λ^2 ))dx with λ≥0 1) detdrmine a explicit form of f(λ) 2) calculate f^′ (λ) at form ofintergral and find its value.

$${let}\:{f}\left(\lambda\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{sin}\left(\:\lambda{e}^{{x}} \:+{e}^{−{x}} \right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx}\:{with}\:\lambda\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{detdrmine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left(\lambda\right)\:{at}\:{form}\:{ofintergral}\:{and}\:{find} \\ $$$${its}\:{value}. \\ $$

Question Number 77751 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((cos(e^x +e^(−x) ))/((x^2 +x+1)^2 ))dx

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

Question Number 77746 Answers: 0 Comments: 4

Master comes after Chess disappeared. Boyka comes after Master disappeared. BK comes after Boyka disappeared. What comes after BK disappeared? 1. A−Team 2. Girlka 3. Bezirksschornsteinfegermeister 4. none from above [A question from NMO 2019 in Madagascar]

$${Master}\:{comes}\:{after}\:{Chess}\:{disappeared}. \\ $$$${Boyka}\:{comes}\:{after}\:{Master}\:{disappeared}. \\ $$$${BK}\:{comes}\:{after}\:{Boyka}\:{disappeared}. \\ $$$${What}\:{comes}\:{after}\:{BK}\:{disappeared}? \\ $$$$\mathrm{1}.\:\:{A}−{Team} \\ $$$$\mathrm{2}.\:\:{Girlka} \\ $$$$\mathrm{3}.\:\:{Bezirksschornsteinfegermeister} \\ $$$$\mathrm{4}.\:\:{none}\:{from}\:{above} \\ $$$$ \\ $$$$\left[{A}\:{question}\:{from}\:{NMO}\:\mathrm{2019}\:{in}\:{Madagascar}\right] \\ $$

Question Number 77745 Answers: 0 Comments: 1

ABC is any triangle. C′ . B′ .A′ are respectively middles of [AB] . [AC] and [BC]. we suppose that AB=c AC=b BC=a. 1) u^(→ ) =a^2 BC^→ +b^(2 ) C^→ A+c^2 AB^→ is a vector Demonstrate that u^→ =(a^2 −b^2 )AC^→ +(c^2 −a^2 )AB^→ . i have done it. 2)Deduct that u^→ is not a null vector.

$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{any}\:\mathrm{triangle}. \\ $$$$\mathrm{C}'\:.\:\mathrm{B}'\:\:.\mathrm{A}'\:\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{middles} \\ $$$$\mathrm{of}\:\left[\mathrm{AB}\right]\:.\:\left[\mathrm{AC}\right]\:\:\mathrm{and}\:\:\left[\mathrm{BC}\right]. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\: \\ $$$$\mathrm{AB}=\mathrm{c}\:\:\:\mathrm{AC}=\mathrm{b}\:\:\:\:\mathrm{BC}=\mathrm{a}. \\ $$$$\left.\mathrm{1}\right)\:\overset{\rightarrow\:} {\mathrm{u}}=\mathrm{a}^{\mathrm{2}} \mathrm{B}\overset{\rightarrow} {\mathrm{C}}+\mathrm{b}^{\mathrm{2}\:} \overset{\rightarrow} {\mathrm{C}A}+\mathrm{c}^{\mathrm{2}} \mathrm{A}\overset{\rightarrow} {\mathrm{B}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}=\left(\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{C}}+\left(\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{B}}. \\ $$$${i}\:{have}\:{done}\:{it}. \\ $$$$\left.\mathrm{2}\right){D}\mathrm{educt}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{null}\:\mathrm{vector}. \\ $$

Question Number 77741 Answers: 1 Comments: 1

Question Number 77739 Answers: 1 Comments: 2

Question Number 77729 Answers: 0 Comments: 0

prove that ∫_(−π) ^π cos(2x) cos(3x) cos(4x)....cos(2005x)dx>0

$${prove}\:{that} \\ $$$$\int_{−\pi} ^{\pi} {cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}\right)\:{cos}\left(\mathrm{4}{x}\right)....{cos}\left(\mathrm{2005}{x}\right){dx}>\mathrm{0} \\ $$

Question Number 77725 Answers: 2 Comments: 4

Question Number 77722 Answers: 1 Comments: 2

how to find n−term from S_n =n^2 +7n+2 ?

$${how}\:{to}\:{find}\: \\ $$$${n}−{term}\:{from} \\ $$$${S}_{{n}} ={n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{2}\:? \\ $$

Question Number 77721 Answers: 0 Comments: 1

Question Number 77716 Answers: 1 Comments: 2

∫sin(x^4 ) dx

$$\int{sin}\left({x}^{\mathrm{4}} \right)\:{dx} \\ $$

Question Number 77681 Answers: 1 Comments: 9

Question Number 77676 Answers: 0 Comments: 0

Please how can we demonstrate that a vector is null... hello

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{can}\:\mathrm{we}\:\mathrm{demonstrate} \\ $$$$\mathrm{that}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{null}... \\ $$$$\mathrm{hello} \\ $$

Question Number 77675 Answers: 1 Comments: 0

∫_( 0) ^( ∞) 3(2x − (3/x))^2 dx

$$\int_{\:\mathrm{0}} ^{\:\:\infty} \:\mathrm{3}\left(\mathrm{2x}\:−\:\frac{\mathrm{3}}{\mathrm{x}}\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$

Question Number 77687 Answers: 0 Comments: 8

given function f(x) =f(x+2) for ∀x∈R if ∫_0 ^2 f(x)dx=B , what value of ∫_3 ^7 f(x+8)dx = ?

$${given}\:{function} \\ $$$${f}\left({x}\right)\:={f}\left({x}+\mathrm{2}\right)\:{for}\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={B}\:,\:{what}\:{value}\:{of} \\ $$$$\underset{\mathrm{3}} {\overset{\mathrm{7}} {\int}}\:{f}\left({x}+\mathrm{8}\right){dx}\:=\:? \\ $$

Question Number 77666 Answers: 0 Comments: 1

how Π=3.14 and what it mean?

$${how}\:\Pi=\mathrm{3}.\mathrm{14}\:{and}\:{what}\:{it}\:{mean}? \\ $$

Question Number 78045 Answers: 0 Comments: 2

old activity shown in my recent activity page, ssems like someone is hindering me from being able to see the recent activity page, i reinstalled the app, problem remains..

$${old}\:{activity}\:{shown}\:{in}\:{my} \\ $$$${recent}\:{activity}\:{page},\:{ssems} \\ $$$${like}\:{someone}\:{is}\:{hindering} \\ $$$${me}\:{from}\:{being}\:{able}\:{to}\:{see}\:{the} \\ $$$${recent}\:{activity}\:{page},\:{i}\:{reinstalled} \\ $$$${the}\:{app},\:{problem}\:{remains}.. \\ $$

Question Number 77655 Answers: 2 Comments: 1

Find the remainder when x + x^(25) + x^(49) + x^(81) is divided by x^3 − 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\:\:\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{25}} \:+\:\mathrm{x}^{\mathrm{49}} \:+\:\mathrm{x}^{\mathrm{81}} \:\:\mathrm{is}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{1} \\ $$

Question Number 77651 Answers: 1 Comments: 4

Question Number 77631 Answers: 1 Comments: 0

x^(log_3 (2)) =(√x)+1

$${x}^{{log}_{\mathrm{3}} \left(\mathrm{2}\right)} =\sqrt{{x}}+\mathrm{1} \\ $$

Question Number 77616 Answers: 0 Comments: 5

Question Number 77614 Answers: 1 Comments: 6

Question Number 77608 Answers: 0 Comments: 0

∫((( ln∣tan(((nx)/2)+(π/4))∣ )^2 )/(x^2 +1)) dx ;n>0

$$\int\frac{\left(\:{ln}\mid{tan}\left(\frac{{nx}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\mid\:\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:\:;{n}>\mathrm{0}\: \\ $$

Question Number 77607 Answers: 0 Comments: 2

Two bell A and B rings in different time interval. Bell A rings in the interval of 8minutes while Bell B rings in the interval of 9minutes. If the two bell rings together for the first time when the time is 10:00am (a) At what time will the two bell ring together again. (b) State and explain two process you will use to help SHS student to solve the problem.

$$\mathrm{Two}\:\mathrm{bell}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{different}\: \\ $$$$\mathrm{time}\:\mathrm{interval}.\:\mathrm{Bell}\:\mathrm{A}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{interval}\:\mathrm{of}\:\mathrm{8minutes}\:\mathrm{while}\:\mathrm{Bell}\:\mathrm{B}\:\mathrm{rings} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{9minutes}.\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{bell}\:\mathrm{rings}\:\mathrm{together}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{time}\:\mathrm{is}\:\mathrm{10}:\mathrm{00am} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{At}\:\mathrm{what}\:\mathrm{time}\:\mathrm{will}\:\mathrm{the}\:\mathrm{two}\:\mathrm{bell}\:\mathrm{ring} \\ $$$$\mathrm{together}\:\mathrm{again}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{State}\:\mathrm{and}\:\mathrm{explain}\:\mathrm{two}\:\mathrm{process}\:\mathrm{you}\: \\ $$$$\mathrm{will}\:\mathrm{use}\:\mathrm{to}\:\mathrm{help}\:\mathrm{SHS}\:\mathrm{student}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\mathrm{the}\:\mathrm{problem}. \\ $$

Question Number 77605 Answers: 0 Comments: 0

how to solve : y′′+p(x)y′+q(x)y=r(x)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:: \\ $$$$\mathrm{y}''+\mathrm{p}\left(\mathrm{x}\right)\mathrm{y}'+\mathrm{q}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{r}\left(\mathrm{x}\right) \\ $$

Question Number 77604 Answers: 2 Comments: 0

given (((a−b)(b−c)(c−a))/((a+b)(b+c)(c+a)))=−(1/(30)) what the value of (b/(a+b))+(c/(b+c))+(a/(c+a)) ?

$${given} \\ $$$$\frac{\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}=−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${what}\:{the}\:{value}\:{of}\: \\ $$$$\frac{{b}}{{a}+{b}}+\frac{{c}}{{b}+{c}}+\frac{{a}}{{c}+{a}}\:? \\ $$

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