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Question Number 115812 Answers: 2 Comments: 4

solve lim_(x→∞) (ζ(x)−1)^(1/x)

$${solve} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\zeta\left({x}\right)−\mathrm{1}\right)^{\frac{\mathrm{1}}{{x}}} \\ $$

Question Number 115798 Answers: 1 Comments: 1

Question Number 115793 Answers: 1 Comments: 0

Given that p_∽ = ((( 2)),((−3)) ) , q_∽ = (((−4)),(( m)) ) and r_∽ = ((n),(4) ) If p_∽ +q_∽ −r_∽ is a unit vector, find the value of m and n.

$$\mathrm{Given}\:\mathrm{that}\:\underset{\backsim} {{p}}=\begin{pmatrix}{\:\:\mathrm{2}}\\{−\mathrm{3}}\end{pmatrix}\:,\:\underset{\backsim} {{q}}=\begin{pmatrix}{−\mathrm{4}}\\{\:\:\:{m}}\end{pmatrix}\:\mathrm{and}\:\underset{\backsim} {{r}}=\begin{pmatrix}{{n}}\\{\mathrm{4}}\end{pmatrix} \\ $$$$\mathrm{If}\:\underset{\backsim} {{p}}+\underset{\backsim} {{q}}−\underset{\backsim} {{r}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{m}\:\mathrm{and}\:{n}. \\ $$

Question Number 115781 Answers: 4 Comments: 0

∫_0 ^(1/( (√2))) ((x sin^(−1) (x^2 ))/( (√(1−x^4 )))) dx =? ∫2^(−x) tanh (2^(1−x) ) dx =?

$$\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} {\int}}\:\frac{{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx}\:=? \\ $$$$\int\mathrm{2}^{−{x}} \:\mathrm{tanh}\:\left(\mathrm{2}^{\mathrm{1}−{x}} \right)\:{dx}\:=? \\ $$

Question Number 115780 Answers: 10 Comments: 1

lim_(x→0) (cos x)^(1/x^2 ) = ? lim_(x→∞) (e^(3x) −5x)^(1/x) =? lim_(x→0) ((e^(2x) −2e^x +1)/(cos 3x−2cos 2x+cos x))=? lim_(x→0) (1/x^2 )−cot^2 x =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:{x}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \:=\:? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({e}^{\mathrm{3}{x}} −\mathrm{5}{x}\right)^{\frac{\mathrm{1}}{{x}}} \:=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{\mathrm{2}{x}} −\mathrm{2}{e}^{{x}} +\mathrm{1}}{\mathrm{cos}\:\mathrm{3}{x}−\mathrm{2cos}\:\mathrm{2}{x}+\mathrm{cos}\:{x}}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\mathrm{cot}\:^{\mathrm{2}} {x}\:=? \\ $$

Question Number 115777 Answers: 3 Comments: 0

lim_(x→0) ((sin x−tan^(−1) x)/(x^2 ln (1+x)))

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}−\mathrm{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} \:\mathrm{ln}\:\left(\mathrm{1}+{x}\right)} \\ $$

Question Number 115775 Answers: 2 Comments: 0

lim_(x→∞) ((((3−(√x))((√x)+2))/(8x−4)))^(1/(3 ))

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\frac{\left(\mathrm{3}−\sqrt{{x}}\right)\left(\sqrt{{x}}+\mathrm{2}\right)}{\mathrm{8}{x}−\mathrm{4}}} \\ $$

Question Number 121180 Answers: 1 Comments: 1

Question Number 115773 Answers: 0 Comments: 0

((1−x)/( (√(x^2 −2x+5)))) = (3/5)

$$\:\frac{\mathrm{1}−{x}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}}}\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$

Question Number 115771 Answers: 2 Comments: 0

y′′−y′−2y=e^(2x) .cos^2 x

$${y}''−{y}'−\mathrm{2}{y}={e}^{\mathrm{2}{x}} .\mathrm{cos}\:^{\mathrm{2}} {x} \\ $$

Question Number 115769 Answers: 1 Comments: 0

There are 3 teachers and 6 students who will sit on the 9 available seats. many arrangements they sit if each teacher is flanked by 2 students

$${There}\:{are}\:\mathrm{3}\:{teachers}\:{and}\:\mathrm{6}\:{students} \\ $$$${who}\:{will}\:{sit}\:{on}\:{the}\:\mathrm{9}\:{available}\:{seats}.\:{many} \\ $$$${arrangements}\:{they}\:{sit}\:{if}\:{each}\: \\ $$$${teacher}\:{is}\:{flanked}\:{by}\:\mathrm{2}\:{students} \\ $$

Question Number 115765 Answers: 1 Comments: 3

Show that sin (α + β) = sin α cos β + cos α sin β.

$$\: \\ $$$$\:\:\:\mathrm{Show}\:\mathrm{that}\:\mathrm{sin}\:\left(\alpha\:+\:\beta\right)\:=\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:+\:\mathrm{cos}\:\alpha\:\mathrm{sin}\:\beta. \\ $$

Question Number 115761 Answers: 2 Comments: 1

.... advanced calculus... ... evaluate ... Ψ= ∫_(−∞) ^( +∞) ((x/(2+2^(−x) +2^x )))^2 dx =??? m.n.july 70

$$\:\:\:\:\:\:....\:\:\:{advanced}\:\:{calculus}...\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:...\:\:\:{evaluate}\:...\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\:\int_{−\infty} ^{\:+\infty} \left(\frac{{x}}{\mathrm{2}+\mathrm{2}^{−{x}} +\mathrm{2}^{{x}} }\right)^{\mathrm{2}} {dx}\:=??? \\ $$$$\:{m}.{n}.{july}\:\mathrm{70} \\ $$$$ \\ $$

Question Number 115830 Answers: 0 Comments: 1

create the differention equation from x^2 +y^2 +2ax+2by+c=0

$${create}\:{the}\:{differention}\:{equation}\:{from} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{ax}+\mathrm{2}{by}+{c}=\mathrm{0} \\ $$

Question Number 115829 Answers: 1 Comments: 0

prove that (y−c)^2 =cx its solution of the differention equation 4xy^(′′) +2xy^′ −y=0 (m.o)

$${prove}\:{that}\:\left({y}−{c}\right)^{\mathrm{2}} ={cx}\:{its}\:{solution}\:{of}\:{the}\:{differention}\:{equation}\:\mathrm{4}{xy}^{''} +\mathrm{2}{xy}^{'} −{y}=\mathrm{0} \\ $$$$\left({m}.{o}\right) \\ $$

Question Number 115750 Answers: 4 Comments: 0

Question Number 115743 Answers: 3 Comments: 0

∫ e^(ax) .sin bx dx =? by complex number

$$\int\:{e}^{{ax}} .\mathrm{sin}\:{bx}\:{dx}\:=? \\ $$$${by}\:{complex}\:{number} \\ $$

Question Number 115742 Answers: 1 Comments: 0

what the cooefficient of x^(10) from (1+x)×(1+2x^2 )×(1+3x^3 )×...×(1+2020x^(2020) )

$${what}\:{the}\:{cooefficient}\:{of}\:{x}^{\mathrm{10}} \:{from} \\ $$$$\left(\mathrm{1}+{x}\right)×\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)×\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)×...×\left(\mathrm{1}+\mathrm{2020}{x}^{\mathrm{2020}} \right) \\ $$

Question Number 115736 Answers: 2 Comments: 0

Question Number 115733 Answers: 3 Comments: 0

Given xy =(1/3) for x,y∈R find min value of (4/x^6 )+(9/y^6 )

$${Given}\:{xy}\:=\frac{\mathrm{1}}{\mathrm{3}}\:{for}\:{x},{y}\in\mathbb{R}\: \\ $$$${find}\:{min}\:{value}\:{of}\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}} } \\ $$

Question Number 115732 Answers: 0 Comments: 1

Question Number 115725 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((lnx)/((x^(2 ) +x+2)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}^{\mathrm{2}\:} +{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 115721 Answers: 2 Comments: 4

(D^2 −6D+9)y = (e^(3x) /x^2 )

$$\left({D}^{\mathrm{2}} −\mathrm{6}{D}+\mathrm{9}\right){y}\:=\:\frac{{e}^{\mathrm{3}{x}} }{{x}^{\mathrm{2}} } \\ $$

Question Number 115714 Answers: 0 Comments: 1

Question Number 115706 Answers: 1 Comments: 3

the area of a square, A(t) is increased at a rate equal to its perimeter write a differential equation that A(t) satisfy , starting from (dA/dt) =

$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square},\:{A}\left({t}\right)\:\mathrm{is}\:\mathrm{increased} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{its}\:\mathrm{perimeter} \\ $$$$\mathrm{write}\:\mathrm{a}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{that}\:{A}\left({t}\right) \\ $$$$\mathrm{satisfy}\:,\:\mathrm{starting}\:\mathrm{from}\:\frac{{dA}}{{dt}}\:= \\ $$

Question Number 115705 Answers: 1 Comments: 0

... nice math ... find :: Φ=∫_0 ^( ∞) (sin(x)−cos(x) )ln(x)dx=???

$$\:\:\:\:\:...\:{nice}\:\:\:{math}\:... \\ $$$$ \\ $$$$\:\:\:\:{find}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\Phi=\int_{\mathrm{0}} ^{\:\infty} \left({sin}\left({x}\right)−{cos}\left({x}\right)\:\right){ln}\left({x}\right){dx}=??? \\ $$$$ \\ $$

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