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Question Number 83028 Answers: 0 Comments: 3

(dy/dx) + y sec x = tan x

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{y}\:\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{tan}\:\mathrm{x} \\ $$

Question Number 83026 Answers: 0 Comments: 0

Prove that 123456..201820192020 divided by 13 , the remainder is 5 .

$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\mathrm{123456}..\mathrm{201820192020}\:\:{divided}\:\:{by}\:\:\mathrm{13}\:\:,\:\:{the} \\ $$$${remainder}\:\:{is}\:\:\mathrm{5}\:. \\ $$

Question Number 83021 Answers: 0 Comments: 0

find the sequence v_n wich verify v_n +v_(n+1) =(((−1)^n )/(√n)) (n≥1) is (v_n ) convergente?

$${find}\:{the}\:{sequence}\:{v}_{{n}} \:{wich}\:{verify}\:{v}_{{n}} +{v}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\sqrt{{n}}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${is}\:\left({v}_{{n}} \right)\:{convergente}? \\ $$

Question Number 83020 Answers: 0 Comments: 0

find the sequence u_n wich verify u_n +u_(n+1) =((sin(n))/n) ∀n>0

$${find}\:{the}\:{sequence}\:{u}_{{n}} \:{wich}\:{verify}\:{u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{{sin}\left({n}\right)}{{n}}\:\:\forall{n}>\mathrm{0} \\ $$

Question Number 83019 Answers: 1 Comments: 1

find lim_(x→0) ((1−(√(1+x+x^2 ))cos(2x))/x^3 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{cos}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{3}} } \\ $$

Question Number 83010 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ch(cos(2x)))/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({cos}\left(\mathrm{2}{x}\right)\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 83009 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(chx))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({chx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 83008 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ch(cosx))/(x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ch}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 82995 Answers: 1 Comments: 1

Question Number 82993 Answers: 1 Comments: 0

Question Number 82991 Answers: 1 Comments: 2

Question Number 82988 Answers: 1 Comments: 3

lim_(x→0) ((1−(√(1+x^2 ))cos x)/x^4 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} \:}\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} } \\ $$

Question Number 82985 Answers: 1 Comments: 0

Question Number 82975 Answers: 0 Comments: 7

To the member in forum. please give an opinion on this matter. George , Lucia and 12 of their friends will sit around a round table. Many of their arrangements sit if George and Lucia always flank 5 of their friends?

$$\mathrm{To}\:\mathrm{the}\:\mathrm{member}\:\mathrm{in}\:\mathrm{forum}.\:\mathrm{please}\: \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{opinion}\:\mathrm{on}\:\mathrm{this}\:\mathrm{matter}. \\ $$$$\mathrm{George}\:,\:\mathrm{Lucia}\:\mathrm{and}\:\mathrm{12}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{friends}\:\mathrm{will}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{Many}\:\mathrm{of}\:\mathrm{their}\:\mathrm{arrangements}\:\mathrm{sit}\: \\ $$$$\mathrm{if}\:\mathrm{George}\:\mathrm{and}\:\mathrm{Lucia}\:\mathrm{always}\:\mathrm{flank} \\ $$$$\mathrm{5}\:\mathrm{of}\:\mathrm{their}\:\mathrm{friends}? \\ $$

Question Number 82974 Answers: 1 Comments: 1

Question Number 82973 Answers: 0 Comments: 0

calculate lim_(n→+∞) ∫_0 ^n (1−(x/n))^n arctan(nx)dx

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

Question Number 82972 Answers: 0 Comments: 0

calculate ∫_0 ^1 arctan(x)ln(1+x)dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 82971 Answers: 1 Comments: 2

1)find ∫ (dx/((x^2 +x+1)^6 )) 2)calculate ∫_(−∞) ^(+∞) (dx/((x^2 +x+1)^6 ))

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$

Question Number 82970 Answers: 0 Comments: 2

1)find ∫ (dx/((x^2 −1)^9 )) 2) calculate ∫_2 ^(+∞) (dx/((x^2 −1)^9 ))

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$

Question Number 82954 Answers: 1 Comments: 3

∫ ((cos 4x−cos 2x)/(sin 4x−cos 2x)) dx

$$\int\:\frac{\mathrm{cos}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$

Question Number 82953 Answers: 0 Comments: 3

verify that: cosh.cosh^(−1) (y) = y, if y ∈ (1, + ∞)

$$\mathrm{verify}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{cosh}.\mathrm{cosh}^{−\mathrm{1}} \left(\mathrm{y}\right)\:\:\:=\:\:\:\mathrm{y},\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{y}\:\:\in\:\:\left(\mathrm{1},\:\:\:+\:\infty\right) \\ $$

Question Number 82952 Answers: 1 Comments: 0

Show that: y + (√(y^2 − 1)) ≥ 1 and 0 < y − (√(y^2 − 1)) ≤ 1 if y ≥ 1

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{y}\:\:+\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\:\geqslant\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{0}\:\:<\:\:\mathrm{y}\:\:−\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\leqslant\:\:\mathrm{1} \\ $$$$\mathrm{if}\:\:\mathrm{y}\:\:\geqslant\:\mathrm{1} \\ $$

Question Number 82944 Answers: 1 Comments: 2

sin^2 (27^o )+sin^2 (87^o )+sin^2 (33^o ) =

$$ \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{27}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{87}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{33}^{\mathrm{o}} \right)\:= \\ $$

Question Number 82937 Answers: 0 Comments: 2

Find the area between the curves y= log x and y= (log x)^2 .

$$\:\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\:\mathrm{y}=\:\mathrm{log}\:\mathrm{x}\:\:\mathrm{and}\:\mathrm{y}=\:\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} . \\ $$

Question Number 82950 Answers: 1 Comments: 1

lim_(x→0) ((((1+tan x))^(1/(3 )) −((1+sin x))^(1/(3 )) )/x^3 ) =

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}\:−\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} }\:=\: \\ $$

Question Number 82929 Answers: 2 Comments: 0

if 2B+A=45° show that; tan B= ((1−2tanA−tan^2 A)/(1+2tanA−tan^2 A))

$${if}\:\mathrm{2}{B}+{A}=\mathrm{45}° \\ $$$${show}\:{that}; \\ $$$${tan}\:{B}=\:\frac{\mathrm{1}−\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}}{\mathrm{1}+\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}} \\ $$

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