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AllQuestion and Answers: Page 1225

Question Number 90049 Answers: 0 Comments: 0

Question Number 90048 Answers: 1 Comments: 0

5^(√x) −5^(x−7) = 100

$$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\mathrm{5}^{\mathrm{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$

Question Number 90046 Answers: 0 Comments: 0

bhz

$${bhz} \\ $$

Question Number 90044 Answers: 0 Comments: 2

calculste ∫_0 ^1 sin([2x] −[(1/x)])dx

$${calculste}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left(\left[\mathrm{2}{x}\right]\:−\left[\frac{\mathrm{1}}{{x}}\right]\right){dx} \\ $$

Question Number 90043 Answers: 0 Comments: 0

calculate f(a) =∫_0 ^∞ ((arctan(ax))/(x^2 +a^2 ))dx with a>0

$${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({ax}\right)}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx}\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 90042 Answers: 0 Comments: 1

calculste I =∫_0 ^(+∞) ((ch(cos(2x))dx)/(x^2 +4)) and J =∫_0 ^∞ ((cos(2chx)dx)/(x^2 +4)) compare I and J

$${calculste}\:{I}\:=\int_{\mathrm{0}} ^{+\infty} \:\frac{{ch}\left({cos}\left(\mathrm{2}{x}\right)\right){dx}}{{x}^{\mathrm{2}} \:+\mathrm{4}} \\ $$$${and}\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}{chx}\right){dx}}{{x}^{\mathrm{2}} \:+\mathrm{4}} \\ $$$${compare}\:{I}\:{and}\:{J} \\ $$

Question Number 90041 Answers: 1 Comments: 0

calculste ∫_0 ^∞ ((xarctan(2x))/(9+2x^2 ))dx

$${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xarctan}\left(\mathrm{2}{x}\right)}{\mathrm{9}+\mathrm{2}{x}^{\mathrm{2}} }{dx}\: \\ $$

Question Number 90040 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) ((ch(acosx +bsinx))/(x^2 −x+1))dx a and b reals given

$${find}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{ch}\left({acosx}\:+{bsinx}\right)}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx} \\ $$$${a}\:{and}\:{b}\:{reals}\:{given} \\ $$

Question Number 90038 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (H_n /n^k )=S_k H_q =Σ_(p=1) ^q (1/p) Is there a simple from for S_k

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{{k}} }={S}_{{k}} \:\:\:\:\:\:\:{H}_{{q}} =\underset{{p}=\mathrm{1}} {\overset{{q}} {\sum}}\frac{\mathrm{1}}{{p}} \\ $$$${Is}\:{there}\:{a}\:{simple}\:{from}\:{for}\:{S}_{{k}} \\ $$

Question Number 90030 Answers: 0 Comments: 0

Question Number 90024 Answers: 0 Comments: 2

sinh^(−1) [ln(x + (√(x^2 + 1)) )] = ?

$$\mathrm{sinh}^{−\mathrm{1}} \left[\mathrm{ln}\left({x}\:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right)\right]\:=\:? \\ $$

Question Number 90023 Answers: 1 Comments: 0

∫ e^(∣x∣) dx = ???

$$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$

Question Number 90019 Answers: 1 Comments: 0

find the gcd(2467, 1367)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{gcd}\left(\mathrm{2467},\:\mathrm{1367}\right) \\ $$

Question Number 90018 Answers: 1 Comments: 2

expand , ln(1 + sin x) right up to the term in x^3

$$\mathrm{expand}\:,\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{sin}\:{x}\right)\:\mathrm{right}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{3}} \\ $$

Question Number 90013 Answers: 1 Comments: 2

−p^2 +2027=−q^2 p+q=?

$$−{p}^{\mathrm{2}} +\mathrm{2027}=−{q}^{\mathrm{2}} \\ $$$${p}+{q}=? \\ $$

Question Number 90011 Answers: 0 Comments: 6

Question Number 90009 Answers: 0 Comments: 0

Σ_(n=0) ^∞ ((((√2)−1)^(2n+1) )/((2n+1)^2 ))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$

Question Number 90003 Answers: 0 Comments: 0

show that ∫_(−∞) ^∞ (dx/(1+(x+tan(x))^(2 ) ))=π

$${show}\:{that} \\ $$$$\int_{−\infty} ^{\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tan}\left({x}\right)\right)^{\mathrm{2}\:} }=\pi \\ $$

Question Number 89994 Answers: 2 Comments: 0

x−y=3(√(xy)) ((x/y)−1)^3 +((y/x)−1)^3 = ?

$$\mathrm{x}−\mathrm{y}=\mathrm{3}\sqrt{\mathrm{xy}} \\ $$$$\left(\frac{\mathrm{x}}{\mathrm{y}}−\mathrm{1}\right)^{\mathrm{3}} +\left(\frac{\mathrm{y}}{\mathrm{x}}−\mathrm{1}\right)^{\mathrm{3}} \:=\:? \\ $$

Question Number 89991 Answers: 0 Comments: 2

if a,b > 0 and (a^2 /b^2 ) = (5/3) find ((a^2 +b^2 )/(ab))

$$\mathrm{if}\:\mathrm{a},\mathrm{b}\:>\:\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{ab}} \\ $$

Question Number 89986 Answers: 0 Comments: 3

∫_0 ^1 (−1)^(⌊(1/x)⌋) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \:{dx} \\ $$

Question Number 89980 Answers: 0 Comments: 2

Question Number 89978 Answers: 0 Comments: 1

(x (dy/dx)−y)(cos (((2y)/x))) = −3x^4

$$\left(\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{2y}}{\mathrm{x}}\right)\right)\:=\:−\mathrm{3x}^{\mathrm{4}} \\ $$

Question Number 89977 Answers: 0 Comments: 2

Question Number 89973 Answers: 1 Comments: 1

x (dy/dx) −y = x^2 tan ((y/x))

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

Question Number 89970 Answers: 0 Comments: 1

xy (dy/dx) = y^2 ((x^3 /(x^2 +1)))

$$\mathrm{xy}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$

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