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Question Number 164639 Answers: 1 Comments: 0

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∫ e^(tan(x)) dx {Z.A}

$$\int\:\boldsymbol{{e}}^{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)} \:\boldsymbol{{dx}} \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{{A}}\right\} \\ $$

Question Number 161450 Answers: 0 Comments: 0

A ector field is given by v= (x^2 −y^2 +x)i−(2xy+y)j. Show that vector v is irrotational hence find the scalar potential

$$\mathrm{A}\: \mathrm{ector}\:\mathrm{field}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{v}= \\ $$$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} +\mathrm{x}\right)\mathrm{i}−\left(\mathrm{2xy}+\mathrm{y}\right)\mathrm{j}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{vector}\:\mathrm{v}\:\mathrm{is}\:\mathrm{irrotational}\:\mathrm{hence}\:\mathrm{find} \\ $$$$\:\mathrm{the}\:\mathrm{scalar}\:\mathrm{potential} \\ $$

Question Number 159748 Answers: 2 Comments: 0

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lim_(x→∞) ((1/(x^2 +1))+(1/(x^2 +4))+(1/(x^2 +9))+…)=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{9}}+\ldots\right)=? \\ $$

Question Number 158081 Answers: 1 Comments: 0

determine the angle between two vectors A=4ax+ay−3az and B=2ax+4ay−3az

$${determine}\:{the}\:{angle}\:{between}\:{two}\:{vectors} \\ $$$${A}=\mathrm{4}{ax}+{ay}−\mathrm{3}{az}\:\:{and}\:\:{B}=\mathrm{2}{ax}+\mathrm{4}{ay}−\mathrm{3}{az} \\ $$

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0< α <(π/2) (( sin(α)))^(1/( 3)) + ((cos(α))^(1/3) )= (( tan(α)))^(1/3) (( tan (α ) + cot (α ))/2) =?

$$ \\ $$$$\:\:\:\:\:\mathrm{0}<\:\alpha\:<\frac{\pi}{\mathrm{2}}\:\:\: \\ $$$$\left.\:\:\sqrt[{\:\mathrm{3}}]{\:{sin}\left(\alpha\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\alpha\right.}\right)=\:\sqrt[{\mathrm{3}}]{\:{tan}\left(\alpha\right)} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\frac{\:{tan}\:\left(\alpha\:\right)\:+\:{cot}\:\left(\alpha\:\right)}{\mathrm{2}}\:=? \\ $$

Question Number 152588 Answers: 3 Comments: 0

∫_(−1 ) ^1 ((3x+4)/(3+4x+3x^2 ))dt please,help me

$$\int_{−\mathrm{1}\:} ^{\mathrm{1}} \frac{\mathrm{3}{x}+\mathrm{4}}{\mathrm{3}+\mathrm{4}{x}+\mathrm{3}{x}^{\mathrm{2}} }{dt} \\ $$$${please},{help}\:{me} \\ $$

Question Number 148151 Answers: 1 Comments: 0

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Ω := ∫_0 ^( 1) Li_( 2) ( (√x) )dx = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \left(\:\sqrt{{x}}\:\right){dx}\:=\:? \\ $$$$ \\ $$

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let f(x,y)=((x^5 y^2 )/(10)) then find D_u f(−5,−3) in the direction of the vector <0,−2>?

$${let}\:{f}\left({x},{y}\right)=\frac{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }{\mathrm{10}}\:{then}\:{find}\: \\ $$$${D}_{{u}} {f}\left(−\mathrm{5},−\mathrm{3}\right)\:{in}\:{the}\:{direction}\:{of}\: \\ $$$${the}\:{vector}\:<\mathrm{0},−\mathrm{2}>? \\ $$

Question Number 146315 Answers: 1 Comments: 0

Question Number 144166 Answers: 1 Comments: 0

Given p^→ =(√2) i^ +2(√3) j^ + (√3) k^ & q^→ =a i^ +j^ +2k^ . If proj_q^→ p^→ = ((2(√2))/9) q^→ then ∣q^→ ∣ =?

$$\mathrm{Given}\:\overset{\rightarrow} {\mathrm{p}}=\sqrt{\mathrm{2}}\:\hat {\mathrm{i}}+\mathrm{2}\sqrt{\mathrm{3}}\:\hat {\mathrm{j}}+\:\sqrt{\mathrm{3}}\:\hat {\mathrm{k}}\:\&\: \\ $$$$\:\overset{\rightarrow} {\mathrm{q}}=\mathrm{a}\:\hat {\mathrm{i}}+\hat {\mathrm{j}}\:+\mathrm{2}\hat {\mathrm{k}}\:.\:\mathrm{If}\:\mathrm{proj}_{\overset{\rightarrow} {\mathrm{q}}} \:\overset{\rightarrow} {\mathrm{p}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{9}}\:\overset{\rightarrow} {\mathrm{q}}\: \\ $$$$\mathrm{then}\:\mid\overset{\rightarrow} {\mathrm{q}}\mid\:=?\: \\ $$

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..........CALCULUS........... prove that:: 𝛗:=Σ_(n=1) ^∞ (((−1)^(n−1) ((n−1)!)^2 )/((2n)!))=2log^2 (ϕ) ϕ=golden ratio.... .............

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:..........{CALCULUS}........... \\ $$$$\:\:\:\:\:\:\:{prove}\:{that}::\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \left(\left({n}−\mathrm{1}\right)!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}=\mathrm{2}{log}^{\mathrm{2}} \left(\varphi\right) \\ $$$$\:\:\:\:\varphi={golden}\:{ratio}.... \\ $$$$\:\:\:\:............. \\ $$

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Let f(x)=((sin(x))/x) , prove that : Σ_(n=0) ^∞ [ f(nπ+α)+f(nπ−α) ]= 1+f(α)

$$\mathrm{Let}\:{f}\left({x}\right)=\frac{{sin}\left({x}\right)}{{x}}\:,\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\:{f}\left({n}\pi+\alpha\right)+{f}\left({n}\pi−\alpha\right)\:\right]=\:\mathrm{1}+{f}\left(\alpha\right) \\ $$

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