Question and Answers Forum

AllQuestion and Answers: Page 1149

Question Number 99023 Answers: 0 Comments: 3

Question Number 99011 Answers: 1 Comments: 2

Question Number 99007 Answers: 2 Comments: 0

Let I_y = ∫_(−2) ^2 [y^3 cos ((y/2)) + (1/2)]((√(4−y^2 )) ) dy then I_y = ???

$$\mathrm{Let}\:{I}_{{y}} \:=\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\left[{y}^{\mathrm{3}} \:\mathrm{cos}\:\left(\frac{{y}}{\mathrm{2}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right]\left(\sqrt{\mathrm{4}−{y}^{\mathrm{2}} }\:\right)\:{dy}\: \\ $$$$\mathrm{then}\:{I}_{{y}} \:=\:??? \\ $$

Question Number 99005 Answers: 2 Comments: 0

Σ_(m = 1) ^∞ Σ_(n = 1) ^∞ (1/(mn(m+n))) ?

$$\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{mn}\left(\mathrm{m}+\mathrm{n}\right)}\:?\: \\ $$

Question Number 99003 Answers: 3 Comments: 0

Given 5x−3y=6 . find min value of (x−1)^2 +(y+1)^2 ?

$${Given}\:\mathrm{5}{x}−\mathrm{3}{y}=\mathrm{6}\:.\:{find}\:{min}\:{value} \\ $$$${of}\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \:? \\ $$

Question Number 98993 Answers: 1 Comments: 0

Use the laplace tranform to solve (d^2 y/dx^2 ) + 5(dy/dx) + 6y = e^(−x) for y = 0, and (dy/dx) = 1 when x = 0

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{tranform}\:\mathrm{to}\:\mathrm{solve}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{5}\frac{{dy}}{{dx}}\:+\:\mathrm{6}{y}\:=\:{e}^{−{x}} \\ $$$$\mathrm{for}\:\:{y}\:=\:\mathrm{0},\:\mathrm{and}\:\frac{{dy}}{{dx}}\:=\:\mathrm{1}\:\mathrm{when}\:{x}\:=\:\mathrm{0} \\ $$

Question Number 98988 Answers: 1 Comments: 0

Find the tangent at the poles for the polar equation r = a sin 2θ.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{at}\:\mathrm{the}\:\mathrm{poles}\:\mathrm{for}\:\mathrm{the}\:\mathrm{polar} \\ $$$$\mathrm{equation}\:{r}\:=\:{a}\:\mathrm{sin}\:\mathrm{2}\theta. \\ $$

Question Number 98986 Answers: 1 Comments: 0

Is the sequence u_n =cos(((nπ)/(20))) divergent?

$$\mathrm{Is}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{u}_{\mathrm{n}} =\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{20}}\right)\:\mathrm{divergent}? \\ $$

Question Number 98984 Answers: 0 Comments: 0

Question Number 98983 Answers: 0 Comments: 2

let a,b,c be positive real numbers such that ab+bc+ac=3 prove the inquality ((a(b^2 +c^2 ))/(a^2 +bc))+((b(c^2 +a^2 ))/(b^2 +ac))+((c(b^2 +a^2 ))/(c^2 +ab))≥3

$${let}\:{a},{b},{c}\:{be}\:{positive}\:{real}\:{numbers}\:{such} \\ $$$${that}\:{ab}+{bc}+{ac}=\mathrm{3}\: \\ $$$${prove}\:{the}\:{inquality} \\ $$$$ \\ $$$$\frac{{a}\left({b}^{\mathrm{2}} +{c}^{\mathrm{2}} \right)}{{a}^{\mathrm{2}} +{bc}}+\frac{{b}\left({c}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{{b}^{\mathrm{2}} +{ac}}+\frac{{c}\left({b}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{{c}^{\mathrm{2}} +{ab}}\geqslant\mathrm{3} \\ $$

Question Number 98968 Answers: 0 Comments: 1

if x^x^x^x^(2020) = 2020. Solve for x

$$\mathrm{if}\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{x}^{\mathrm{2020}} } } } =\:\mathrm{2020}.\:\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 98967 Answers: 1 Comments: 0

solve: (((∫_2 ^6 x(√(1+9⌊x⌋^2 ))dx)/(∫_0 ^1 x{(1/x)}⌈(1/x)⌉dx)))(Σ_(n≥1) (−1)^n ((Π_(j=1) ^n ((3/2)−j))/((2n+1)n!)))

$${solve}: \\ $$$$\left(\frac{\int_{\mathrm{2}} ^{\mathrm{6}} {x}\sqrt{\mathrm{1}+\mathrm{9}\lfloor{x}\rfloor^{\mathrm{2}} }{dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} {x}\left\{\frac{\mathrm{1}}{{x}}\right\}\lceil\frac{\mathrm{1}}{{x}}\rceil{dx}}\right)\left(\underset{{n}\geqslant\mathrm{1}} {\sum}\left(−\mathrm{1}\right)^{{n}} \frac{\prod_{{j}=\mathrm{1}} ^{{n}} \left(\frac{\mathrm{3}}{\mathrm{2}}−{j}\right)}{\left(\mathrm{2}{n}+\mathrm{1}\right){n}!}\right) \\ $$

Question Number 98955 Answers: 2 Comments: 2

lim_(x→0) (√(x+(√(x+(√(x+(√(x+∙∙∙))))))))

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\centerdot\centerdot\centerdot}}}} \\ $$

Question Number 98953 Answers: 2 Comments: 0

Given f(x)=sin^2 x find the expansion of f(x) up to the n^(th) term.

$$\mathcal{G}\mathrm{iven}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{find}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}. \\ $$

Question Number 98952 Answers: 0 Comments: 1

Without using L′Ho^ pital′s rule or Maclaurin′s expansion series, find lim_(x→0) ((((xe^x )/(e^x −1))−1)/x)

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}\:\mathrm{or}\:\mathrm{Maclaurin}'\mathrm{s}\:\mathrm{expansion} \\ $$$$\mathrm{series},\:\mathrm{find}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{xe}^{\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}−\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 98951 Answers: 0 Comments: 1

∫tan^(1/5) x.cotx.secxdx

$$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {x}.{cotx}.{secxdx} \\ $$

Question Number 98945 Answers: 0 Comments: 0

calculate lim_(n→+∞) ∫_0 ^n (1−(t/n))^n arctan(nt)dt

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{\mathrm{n}} \left(\mathrm{1}−\frac{\mathrm{t}}{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{arctan}\left(\mathrm{nt}\right)\mathrm{dt} \\ $$

Question Number 98944 Answers: 1 Comments: 0

let g(x) =((cosx +1)/(cos(2x)−3)) developp f at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{cosx}\:+\mathrm{1}}{\mathrm{cos}\left(\mathrm{2x}\right)−\mathrm{3}}\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 98943 Answers: 2 Comments: 0

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

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

Question Number 98942 Answers: 3 Comments: 2

calculate ∫ ((x+1−(√(2x+3)))/(x−2 +(√(x+1)))) dx

$$\mathrm{calculate}\:\int\:\frac{\mathrm{x}+\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{x}−\mathrm{2}\:+\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$

Question Number 98940 Answers: 2 Comments: 1

if (1/((1+x)^n )) =Σ_(m=0) ^∞ a_m x^m determinate a_m

$$\mathrm{if}\:\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} }\:=\sum_{\mathrm{m}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{m}} \mathrm{x}^{\mathrm{m}} \:\:\:\:\mathrm{determinate}\:\mathrm{a}_{\mathrm{m}} \\ $$

Question Number 98932 Answers: 0 Comments: 0

Question Number 98929 Answers: 0 Comments: 6

Find[]the[]integral[]of[] ∫(dt/(√((1+t^(10) ))))

$${Find}\left[\right]{the}\left[\right]{integral}\left[\right]{of}\left[\right] \\ $$$$ \\ $$$$\int\frac{{dt}}{\sqrt{\left(\mathrm{1}+{t}^{\mathrm{10}} \right)}} \\ $$

Question Number 98925 Answers: 1 Comments: 1

If the curve shown below has the equation, y=(x−p)(x^3 −bx−c) then find q/p in terms of b and c.

$${If}\:{the}\:{curve}\:{shown}\:{below}\:{has}\:{the}\: \\ $$$${equation},\:\:{y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{bx}−{c}\right) \\ $$$${then}\:{find}\:\:{q}/{p}\:\:{in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$

Question Number 98924 Answers: 0 Comments: 0

Prove that if a+ bi is a root to pz^2 + qz + r = 0 , where a,b,p,q,r ∈R then a−bi is also a root to that equation.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{a}+\:{bi}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to} \\ $$$$\:{pz}^{\mathrm{2}} \:+\:{qz}\:+\:{r}\:=\:\mathrm{0}\:,\:\mathrm{where}\:{a},{b},{p},{q},{r}\:\in\mathbb{R} \\ $$$$\mathrm{then}\:{a}−{bi}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to}\:\mathrm{that}\:\mathrm{equation}. \\ $$

Question Number 98938 Answers: 2 Comments: 0

Pg 1144 Pg 1145 Pg 1146 Pg 1147 Pg 1148 Pg 1149 Pg 1150 Pg 1151 Pg 1152 Pg 1153

Contact: info@tinkutara.com