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Question Number 138276 Answers: 0 Comments: 0

1) calculate A_n =∫∫_([0,n[^2 ) ((dxdy)/((2x^2 +3y^2 )^2 )) 2)find lim_(n→+∞) A_n

$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}_{\mathrm{n}} =\int\int_{\left[\mathrm{0},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\frac{\mathrm{dxdy}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{3y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{A}_{\mathrm{n}} \\ $$

Question Number 138240 Answers: 3 Comments: 0

(x−1)(dy/dx) +xy = 2xe^(−x)

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

Question Number 138257 Answers: 1 Comments: 0

hi ! calculate : ∫∫_A (x^2 −y^2 )dxdy with A={(x^2 /a^2 ) + (y^2 /b^2 ) ≤ 1}

$$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{calculate}}\::\: \\ $$$$\int\int_{\mathrm{A}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dxdy}\:{with}\:\mathrm{A}=\left\{\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\leqslant\:\mathrm{1}\right\} \\ $$

Question Number 138254 Answers: 0 Comments: 10

Question Number 138250 Answers: 1 Comments: 0

(x^2 −10x+6)^(x−2) >1

$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{10x}+\mathrm{6}\right)^{\mathrm{x}−\mathrm{2}} >\mathrm{1} \\ $$

Question Number 138249 Answers: 1 Comments: 0

lim_(n→0) ((2^(n+1) +3^(n+2) +4^(n+3) )/(2^n +3^n +4^n ))

$$\mathrm{li}\underset{\mathrm{n}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} +\mathrm{3}^{\mathrm{n}+\mathrm{2}} +\mathrm{4}^{\mathrm{n}+\mathrm{3}} }{\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} } \\ $$

Question Number 138248 Answers: 0 Comments: 3

x^(x+4) =32

$$\mathrm{x}^{\mathrm{x}+\mathrm{4}} =\mathrm{32} \\ $$

Question Number 138236 Answers: 0 Comments: 5

prove that (e^(−2y) /(1+e^(−2y) ))<∣tan(z) − i∣<(e^(−2y) /(1−e^(−2y) )) ,y>0 how can solve this ?

$${prove}\:{that}\: \\ $$$$ \\ $$$$\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}+{e}^{−\mathrm{2}{y}} }<\mid{tan}\left({z}\right)\:−\:{i}\mid<\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}−{e}^{−\mathrm{2}{y}} }\:\:\:,{y}>\mathrm{0} \\ $$$$ \\ $$$${how}\:{can}\:{solve}\:{this}\:? \\ $$

Question Number 138235 Answers: 1 Comments: 0

for p,q∈R satisfying p^4 +q^4 =4pq find the range of p+q when 1) no restriction 2) 0≤p≤1, 0≤q≤1

$${for}\:{p},{q}\in\mathbb{R}\:{satisfying}\:{p}^{\mathrm{4}} +{q}^{\mathrm{4}} =\mathrm{4}{pq} \\ $$$${find}\:{the}\:{range}\:{of}\:{p}+{q}\:{when} \\ $$$$\left.\mathrm{1}\right)\:{no}\:{restriction} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{0}\leqslant{p}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{q}\leqslant\mathrm{1} \\ $$

Question Number 138231 Answers: 0 Comments: 0

Question Number 138224 Answers: 1 Comments: 1

Question Number 138223 Answers: 2 Comments: 0

.......nice ... ... ... calculus... evaluate ::: 𝚯=Σ_(n=−∞) ^∞ (1/((3n+1)^3 )) =? .........................

$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:.......{nice}\:...\:...\:...\:{calculus}... \\ $$$$\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\Theta}=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:......................... \\ $$

Question Number 138219 Answers: 2 Comments: 0

Consider the function y=((x^2 +3x+6)/(3x−1)) 1) Determine the intercept of the function 2) Find the asymptotes if they exist 3) find the turning point and determine the type of turnin point they are. 4) sketch the graph of the function.

Question Number 138209 Answers: 2 Comments: 1

I_n =∫_0 ^( 1) x^n (√(x^2 +1))dx find reduction formula

$${I}_{{n}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}} \sqrt{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$${find}\:{reduction}\:{formula} \\ $$

Question Number 138206 Answers: 1 Comments: 1

Question Number 138205 Answers: 2 Comments: 3

Question Number 138203 Answers: 1 Comments: 0

Three circles each radius 1, touch one another externally and they lie between two parallel line. The minimum possible distance between the lines is _

$${Three}\:{circles}\:{each}\:{radius}\:\mathrm{1},\:{touch}\:{one} \\ $$$${another}\:{externally}\:{and}\:{they}\:{lie} \\ $$$${between}\:{two}\:{parallel}\:{line}.\:{The}\: \\ $$$${minimum}\:{possible}\:{distance}\:{between}\: \\ $$$${the}\:{lines}\:{is}\:\_\: \\ $$

Question Number 142191 Answers: 1 Comments: 3

Question Number 142185 Answers: 2 Comments: 0

∫(1/(x^4 +1))dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 138193 Answers: 1 Comments: 0

Given x≠y and x^2 =25x+y, y^2 =x+25y solve for the value of (√(x^2 +y^2 +1)) without using calculators or tools. Show your method.

$${Given}\:{x}\neq{y}\:{and}\:{x}^{\mathrm{2}} =\mathrm{25}{x}+{y},\:{y}^{\mathrm{2}} ={x}+\mathrm{25}{y}\: \\ $$$${solve}\:{for}\:{the}\:{value}\:{of}\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}}\:{without}\: \\ $$$${using}\:{calculators}\:{or}\:{tools}. \\ $$$${Show}\:{your}\:{method}. \\ $$

Question Number 138217 Answers: 0 Comments: 2

A rectangular water tank is being filed at the constant rate of 70lt/s. The base of the tank has width w=9m and length length l=16m if the volume of the tank is v=w×l×h where h is the hight of the tank. what is the rate of change of the hight of water in the tank

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{water}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{being}\:\mathrm{filed} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{70lt}/\mathrm{s}.\:\mathrm{The}\: \\ $$$$\mathrm{base}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{has}\:\mathrm{width}\:\mathrm{w}=\mathrm{9m} \\ $$$$\mathrm{and}\:\mathrm{length}\:\mathrm{length}\:\mathrm{l}=\mathrm{16m}\:\mathrm{if}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{v}=\mathrm{w}×\mathrm{l}×\mathrm{h}\:\mathrm{where}\:\mathrm{h}\:\mathrm{is}\: \\ $$$$\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate} \\ $$$$\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{tank} \\ $$

Question Number 138175 Answers: 1 Comments: 1

Question Number 138171 Answers: 0 Comments: 0

.......mathematical....analysis....... if : 𝛗=∫_0 ^( 1) ((arctan(x).ln(1+x^2 ))/x^2 )dx =(1/(48))(aπ^2 −bπln(2)+c ln^2 (2)) ......then .... a^2 +(b−c+1)^2 =???

$$\:\:\:\:\:\:\:\:\:\:\:.......{mathematical}....{analysis}....... \\ $$$$\:\:\:\:\:{if}\::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{48}}\left({a}\pi^{\mathrm{2}} −{b}\pi{ln}\left(\mathrm{2}\right)+{c}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:......{then}\:\:....\:{a}^{\mathrm{2}} +\left({b}−{c}+\mathrm{1}\right)^{\mathrm{2}} =??? \\ $$

Question Number 138167 Answers: 2 Comments: 0

let f(x) = determinant ((x,x^2 ,x^3 ),(0,(2x ),(3x^2 )),(1,0,x)) find f ′(x)

$$\mathrm{let}\:{f}\left({x}\right)\:=\:\begin{vmatrix}{{x}}&{{x}^{\mathrm{2}} }&{{x}^{\mathrm{3}} }\\{\mathrm{0}}&{\mathrm{2}{x}\:}&{\mathrm{3}{x}^{\mathrm{2}} }\\{\mathrm{1}}&{\mathrm{0}}&{{x}}\end{vmatrix}\:\mathrm{find} \\ $$$$\:{f}\:'\left({x}\right)\: \\ $$

Question Number 138163 Answers: 1 Comments: 0

........nice ... .... .... calculus..... prove that:: Ψ=Σ_(n=1) ^∞ ((1/(n^2 π^2 +1)))=^(???) (1/(e^2 −1)) .............

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:........{nice}\:\:...\:....\:....\:{calculus}..... \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \pi^{\mathrm{2}} +\mathrm{1}}\right)\overset{???} {=}\frac{\mathrm{1}}{{e}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:............. \\ $$

Question Number 138159 Answers: 1 Comments: 0

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