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Question Number 36024 Answers: 1 Comments: 2

Question Number 36021 Answers: 0 Comments: 0

Prove that the hypotenuse never be even of a right angled triangle whose positive integer sides are relatively prime.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{hypotenuse}\:\mathrm{never}\:\mathrm{be} \\ $$$$\mathrm{even}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle}\:\mathrm{whose} \\ $$$$\mathrm{positive}\:\mathrm{integer}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{relatively}\:\mathrm{prime}. \\ $$

Question Number 36019 Answers: 3 Comments: 0

If a+b+c=0 show that ((a/(b−c))+(b/(c−a))+(c/(a−b)))(((b−c)/a)+((c−a)/b) +((a−b)/c))=9

$${If}\:{a}+{b}+{c}=\mathrm{0}\:{show}\:{that} \\ $$$$\left(\frac{{a}}{{b}−{c}}+\frac{{b}}{{c}−{a}}+\frac{{c}}{{a}−{b}}\right)\left(\frac{{b}−{c}}{{a}}+\frac{{c}−{a}}{{b}}\:+\frac{{a}−{b}}{{c}}\right)=\mathrm{9} \\ $$

Question Number 36018 Answers: 1 Comments: 0

Find the value of lim_(x→(π/2)) ((sinx−(sinx)^(sinx) )/(1−sinx+lnsinx))

$${Find}\:{the}\:{value}\:{of} \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {{lim}}\:\frac{{sinx}−\left({sinx}\right)^{{sinx}} }{\mathrm{1}−{sinx}+{lnsinx}} \\ $$

Question Number 36011 Answers: 0 Comments: 2

simplify: ′interval number′ (1,6)∪(3,7)

$$\mathrm{simplify}:\:\:'{interval}\:{number}' \\ $$$$\left(\mathrm{1},\mathrm{6}\right)\cup\left(\mathrm{3},\mathrm{7}\right) \\ $$

Question Number 36010 Answers: 0 Comments: 2

let f(x)= (x/(x^2 +x+1)) 1) calculate f^((n)) (0) 2) developp f at integr serie .

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

Question Number 36009 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((xdx)/((2x+1+i)^3 )) with i^2 =−1 .

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{xdx}}{\left(\mathrm{2}{x}+\mathrm{1}+{i}\right)^{\mathrm{3}} }\:\:{with}\:{i}^{\mathrm{2}} \:=−\mathrm{1}\:. \\ $$

Question Number 35990 Answers: 0 Comments: 2

calculate ∫_2 ^5 ((xdx)/(2x+1 +(√(x−1))))

$${calculate}\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\frac{{xdx}}{\mathrm{2}{x}+\mathrm{1}\:+\sqrt{{x}−\mathrm{1}}} \\ $$

Question Number 35988 Answers: 1 Comments: 2

let f(x) = ((x+2)/(x^3 −4x +3)) 1) calculate f^((n)) (x) 2) developp f at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35987 Answers: 0 Comments: 4

let f(x) = (1/(1+x^3 )) 1) calculate f^((n)) (x) 2) developp f at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{3}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35986 Answers: 0 Comments: 5

let f(x)= (√(1 +n x^2 )) −nx +3 with n integr 1) calculate lim_(x→+∞) and lim_(x→−∞) f(x) 2) calculate f^′ (x) 3) give the equation of assymptote of f at point A(1,f(1)) . 4)calculate lim_(x→+∞) ((f(x))/x) and lim_(x→−∞) ((f(x))/x) .

$${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{1}\:+{n}\:{x}^{\mathrm{2}} }\:\:\:−{nx}\:+\mathrm{3}\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{equation}\:{of}\:{assymptote}\:{of}\:{f}\:{at} \\ $$$${point}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right)\:. \\ $$$$\left.\mathrm{4}\right){calculate}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{f}\left({x}\right)}{{x}}\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\frac{{f}\left({x}\right)}{{x}}\:. \\ $$

Question Number 35983 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((2(√t) +1)/(t^5 +3))dt .

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{\mathrm{2}\sqrt{{t}}\:+\mathrm{1}}{{t}^{\mathrm{5}} \:\:\:+\mathrm{3}}{dt}\:\:. \\ $$

Question Number 35982 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ e^(−arctsn( 1+tx^2 )) dx with t from R 1) calculate f^′ (t) 2) find a simple form of f(t) .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−{arctsn}\left(\:\mathrm{1}+{tx}^{\mathrm{2}} \right)} {dx}\:\:{with}\:{t}\:{from}\:{R} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right)\:. \\ $$

Question Number 36003 Answers: 2 Comments: 0

x [(2),(1) ]+y [(3),(5) ]+ [((−8)),((−11)) ]=0 find x and y

$${x}\begin{bmatrix}{\mathrm{2}}\\{\mathrm{1}}\end{bmatrix}+{y}\begin{bmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{bmatrix}+\begin{bmatrix}{−\mathrm{8}}\\{−\mathrm{11}}\end{bmatrix}=\mathrm{0} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$

Question Number 35968 Answers: 2 Comments: 1

Question Number 35960 Answers: 0 Comments: 3

Solve using Residue Theorem I = ∫_(−∞) ^(+∞) (x^2 /(x^4 + 16)) dx

$$\mathrm{Solve}\:\mathrm{using}\:\mathrm{Residue}\:\mathrm{Theorem} \\ $$$$\mathrm{I}\:=\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:+\:\mathrm{16}}\:{dx} \\ $$

Question Number 35951 Answers: 1 Comments: 3

(cosθ+cosβ/sinθ−sinβ)=(sinθ+sinβ/cosθ−cosβ) prove ghis

$$\left({cos}\theta+{cos}\beta/{sin}\theta−{sin}\beta\right)=\left({sin}\theta+{sin}\beta/{cos}\theta−{cos}\beta\right)\:{prove}\:{ghis} \\ $$

Question Number 35949 Answers: 1 Comments: 1

∫_0 ^( α) ((tan θ)/(√(a^2 cos^2 θ−b^2 sin^2 θ))) dθ = ?

$$\int_{\mathrm{0}} ^{\:\:\alpha} \frac{\mathrm{tan}\:\theta}{\sqrt{{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta−{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta}}\:{d}\theta\:=\:? \\ $$

Question Number 35940 Answers: 1 Comments: 1

Question Number 35939 Answers: 1 Comments: 0

lim_(x→4) ( ((asin (x−4) + cos πx −1)/(x−4)) )^((x−2)/(x−3)) = 4 Find ′a′ ?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\left(\:\frac{{a}\mathrm{sin}\:\left({x}−\mathrm{4}\right)\:+\:\mathrm{cos}\:\pi{x}\:−\mathrm{1}}{{x}−\mathrm{4}}\:\right)^{\frac{{x}−\mathrm{2}}{{x}−\mathrm{3}}} =\:\mathrm{4} \\ $$$${Find}\:'{a}'\:? \\ $$

Question Number 35933 Answers: 1 Comments: 0

differentiate from the first principle y=(1/(√x))

$$\boldsymbol{\mathrm{differentiate}}\:\boldsymbol{\mathrm{from}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{principle}} \\ $$$$\boldsymbol{\mathrm{y}}=\frac{\mathrm{1}}{\sqrt{\boldsymbol{{x}}}} \\ $$

Question Number 35920 Answers: 1 Comments: 1

∫ ((e^(2x) +1)/(2e^x −1)) dx = ?

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

Question Number 35915 Answers: 1 Comments: 0

if P(A) and P(B) are independent events then P(A∣B)=??

$${if}\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent} \\ $$$${events}\:{then}\:{P}\left({A}\mid{B}\right)=?? \\ $$

Question Number 35909 Answers: 1 Comments: 4

∫((7x−6)/((x^2 +25)(√((x−3)^2 +4)))) dx = ?

$$\int\frac{\mathrm{7}{x}−\mathrm{6}}{\left({x}^{\mathrm{2}} +\mathrm{25}\right)\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:=\:? \\ $$

Question Number 35899 Answers: 0 Comments: 2

Evaluate log_(√2) 4+log_(1/2) 16−log_4 32

$${Evaluate}\:{log}_{\sqrt{\mathrm{2}}} \mathrm{4}+{log}_{\mathrm{1}/\mathrm{2}} \mathrm{16}−{log}_{\mathrm{4}} \mathrm{32} \\ $$

Question Number 35897 Answers: 0 Comments: 2

log_x^(1/2 ) 64=3. What is x?

$${log}_{{x}^{\mathrm{1}/\mathrm{2}\:} } \mathrm{64}=\mathrm{3}.\:{What}\:{is}\:{x}? \\ $$

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