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Question Number 55214 Answers: 1 Comments: 1

let U_n =∫_(1/n) ^1 (√(x^2 +(3/n)))dx .calculate lim_(n→+∞) U_n

$${let}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\frac{\mathrm{3}}{{n}}}{dx}\:\:\:.{calculate}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$

Question Number 55211 Answers: 1 Comments: 0

Question Number 55205 Answers: 0 Comments: 0

Please, can you help me with the following? A boat B is found at 40km at at the east of a boat A. A is moving at 30° east at 20km/h, B is moving qt 10km/h at 30°west. After how many hours will the two boats be the closest to each other? What will therefore be the position of the boat B and the boat A? Thank you

$$\mathrm{Please},\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{following}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{boat}\:\boldsymbol{\mathrm{B}}\:\mathrm{is}\:\mathrm{found}\:\mathrm{at}\:\mathrm{40km}\:\mathrm{at}\:\mathrm{at}\:\mathrm{the}\:\mathrm{east}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{boat}\:\boldsymbol{\mathrm{A}}.\:\boldsymbol{\mathrm{A}}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{at}\:\mathrm{30}°\:\mathrm{east}\:\mathrm{at}\:\mathrm{20km}/\mathrm{h}, \\ $$$$\boldsymbol{\mathrm{B}}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{qt}\:\mathrm{10km}/\mathrm{h}\:\mathrm{at}\:\mathrm{30}°\mathrm{west}. \\ $$$$ \\ $$$$\mathrm{After}\:\mathrm{how}\:\mathrm{many}\:\mathrm{hours}\:\mathrm{will}\:\mathrm{the}\:\mathrm{two}\:\mathrm{boats} \\ $$$$\mathrm{be}\:\mathrm{the}\:\mathrm{closest}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{therefore}\:\mathrm{be}\:\mathrm{the}\:\mathrm{position}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{boat}\:\boldsymbol{\mathrm{B}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{boat}\:\boldsymbol{\mathrm{A}}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$$$ \\ $$

Question Number 55198 Answers: 2 Comments: 1

x^5 −4x^4 +6x^3 +8x−32=0 Find at least one root.

$${x}^{\mathrm{5}} −\mathrm{4}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{3}} +\mathrm{8}{x}−\mathrm{32}=\mathrm{0} \\ $$$${Find}\:{at}\:{least}\:{one}\:{root}. \\ $$

Question Number 55197 Answers: 0 Comments: 4

∫(dα/(1−sin^3 α))=? ∫(dβ/(1−cos^3 β))=? ∫(dγ/(1−tan^3 γ))=?

$$\int\frac{{d}\alpha}{\mathrm{1}−\mathrm{sin}^{\mathrm{3}} \:\alpha}=? \\ $$$$\int\frac{{d}\beta}{\mathrm{1}−\mathrm{cos}^{\mathrm{3}} \:\beta}=? \\ $$$$\int\frac{{d}\gamma}{\mathrm{1}−\mathrm{tan}^{\mathrm{3}} \:\gamma}=? \\ $$

Question Number 55195 Answers: 1 Comments: 0

x^2 +ax+(√2)b=0,has 2 roots:c and d,also x^2 +cx+(√2)d=0,has 2 roots:a and b.such that:a, b, c, d,are defferent non zero numbers. find possible value(s) for:a^2 +b^2 +c^2 +d^2 .

Question Number 55193 Answers: 1 Comments: 0

Question Number 55192 Answers: 1 Comments: 1

what will be the numbers of zeroes in the expension of a) 100!×25! b) 100!+25! please help

$${what}\:{will}\:{be}\:{the}\:{numbers}\:{of}\:{zeroes}\:{in}\:{the}\:{expension}\:{of} \\ $$$$\left.{a}\right)\:\mathrm{100}!×\mathrm{25}! \\ $$$$\left.{b}\right)\:\mathrm{100}!+\mathrm{25}! \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 55191 Answers: 2 Comments: 0

Question Number 55185 Answers: 0 Comments: 3

Question Number 55174 Answers: 0 Comments: 3

center and radius convergence of series Σ_(n=0) ^(∝) (((4−2i)/(1+5i)))^n z^n is...

$$\mathrm{center}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{convergence} \\ $$$$\:\mathrm{of}\:\mathrm{series}\:\underset{{n}=\mathrm{0}} {\overset{\propto} {\Sigma}}\:\left(\frac{\mathrm{4}−\mathrm{2}{i}}{\mathrm{1}+\mathrm{5}{i}}\right)^{{n}} {z}^{{n}} \:\mathrm{is}... \\ $$$$ \\ $$

Question Number 55172 Answers: 1 Comments: 0

Question Number 55171 Answers: 0 Comments: 3

Question Number 55166 Answers: 1 Comments: 0

Question Number 55190 Answers: 1 Comments: 0

Question Number 55150 Answers: 2 Comments: 0

Question Number 55149 Answers: 1 Comments: 0

Question Number 55141 Answers: 2 Comments: 1

prove the following identities a.((sin θ)/(1+cos 2θ))=tan θ b.((1−cos 2θ−sin θ)/(sin 2θ−cos θ))=tan θ c.((cos (x+y)+sin (x−y))/(cos 2ycos 2x))=(1/(cos (x+y)sin (y−x)))

$${prove}\:{the}\:{following}\:{identities} \\ $$$$ \\ $$$${a}.\frac{\mathrm{sin}\:\theta}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}\theta}=\mathrm{tan}\:\theta \\ $$$${b}.\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}\theta−\mathrm{sin}\:\theta}{\mathrm{sin}\:\mathrm{2}\theta−\mathrm{cos}\:\theta}=\mathrm{tan}\:\theta \\ $$$${c}.\frac{\mathrm{cos}\:\left({x}+{y}\right)+\mathrm{sin}\:\left({x}−{y}\right)}{\mathrm{cos}\:\mathrm{2}{y}\mathrm{cos}\:\mathrm{2}{x}}=\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}+{y}\right)\mathrm{sin}\:\left({y}−{x}\right)} \\ $$

Question Number 55138 Answers: 0 Comments: 1