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Question Number 81586    Answers: 1   Comments: 6

Dear mister Tanmay y ′′ − y′ −6y = 2sin 3x find solution let y = e^(mx) ? or not

$${Dear}\:{mister}\: \\ $$$${Tanmay} \\ $$$${y}\:''\:−\:{y}'\:−\mathrm{6}{y}\:=\:\mathrm{2sin}\:\mathrm{3}{x}\: \\ $$$${find}\:{solution} \\ $$$$\: \\ $$$${let}\:{y}\:=\:{e}^{{mx}} \:?\:{or}\:{not}\: \\ $$$$ \\ $$

Question Number 81857    Answers: 0   Comments: 2

Question Number 81565    Answers: 1   Comments: 2

If f(x)= (tan x)^(cot x) + (cot x)^(tan x) f ′(x)= ?

$${If}\:{f}\left({x}\right)=\:\left(\mathrm{tan}\:{x}\right)^{\mathrm{cot}\:{x}} \:+\:\left(\mathrm{cot}\:{x}\right)^{\mathrm{tan}\:{x}} \\ $$$${f}\:'\left({x}\right)=\:? \\ $$

Question Number 81562    Answers: 1   Comments: 2

Question Number 81549    Answers: 0   Comments: 5

∫_0 ^4 ⌊x⌋^2 dx = ∫_0 ^4 ⌊x^2 ⌋dx=

$$\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\lfloor\mathrm{x}\rfloor^{\mathrm{2}} \:\mathrm{dx}\:=\: \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\lfloor\mathrm{x}^{\mathrm{2}} \rfloor\mathrm{dx}= \\ $$

Question Number 81545    Answers: 0   Comments: 3

Question Number 81558    Answers: 0   Comments: 2

lim_(x→∞) ((e^x +cos x+ln(x^2 −2x+3))/x) =

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

Question Number 81554    Answers: 2   Comments: 0

y′′′ +4y′ = 3x−1 what is solution

$${y}'''\:+\mathrm{4}{y}'\:=\:\mathrm{3}{x}−\mathrm{1} \\ $$$${what}\:{is}\:{solution} \\ $$

Question Number 81552    Answers: 0   Comments: 3

Question Number 81564    Answers: 0   Comments: 11

given ((a+b)/c) + ((a+c)/b) +((b+c)/a) = 9 a^2 +b^2 +c^2 = 12 maximum value of a+b+c is

$${given}\: \\ $$$$\frac{{a}+{b}}{{c}}\:+\:\frac{{a}+{c}}{{b}}\:+\frac{{b}+{c}}{{a}}\:=\:\mathrm{9} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{12}\: \\ $$$${maximum}\:{value}\:{of}\:{a}+{b}+{c}\:{is} \\ $$

Question Number 81532    Answers: 1   Comments: 3

Question Number 81523    Answers: 0   Comments: 2

Question Number 81519    Answers: 1   Comments: 4

∣∣∣x∣−3∣−2∣=1 solve for real x.

$$\mid\mid\mid{x}\mid−\mathrm{3}\mid−\mathrm{2}\mid=\mathrm{1} \\ $$$${solve}\:{for}\:{real}\:{x}. \\ $$

Question Number 81518    Answers: 0   Comments: 0

Question Number 81514    Answers: 0   Comments: 0

Hello sirs ... what are the graphic maker Apps can you suggest me for my android phone ...please.

$${Hello}\:{sirs}\:...\:{what}\:{are}\:{the}\:{graphic} \\ $$$${maker}\:{Apps}\:{can}\:{you}\:{suggest}\:{me}\: \\ $$$${for}\:{my}\:{android}\:{phone}\:...{please}. \\ $$

Question Number 81507    Answers: 0   Comments: 1

Question Number 81506    Answers: 0   Comments: 4

Question Number 81498    Answers: 1   Comments: 0

what the formula a^ × (b^ ×c^ ) ?

$$\mathrm{what}\:\mathrm{the}\:\mathrm{formula} \\ $$$$\bar {\mathrm{a}}\:×\:\left(\bar {\mathrm{b}}×\bar {\mathrm{c}}\right)\:? \\ $$

Question Number 81485    Answers: 2   Comments: 7

Question Number 81482    Answers: 1   Comments: 1

Evaluate ∫_(−∞) ^∞ (dx/(x^2 +4x+13)).

$${Evaluate}\:\:\int_{−\infty} ^{\infty} \frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}. \\ $$

Question Number 81471    Answers: 0   Comments: 1

prove that tan (x) = sinh (y) if sin (x)= tanh (y).

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)\:=\:\mathrm{sinh}\:\left(\mathrm{y}\right)\:\mathrm{if}\:\mathrm{sin}\:\left(\mathrm{x}\right)= \\ $$$$\mathrm{tanh}\:\left(\mathrm{y}\right). \\ $$

Question Number 81470    Answers: 1   Comments: 0

Prove that the locus of the point of intersection of perpendicular tangents to an ellipse is another ellipse.

$${Prove}\:{that}\:{the}\:{locus}\:{of}\:{the}\:{point} \\ $$$${of}\:{intersection}\:{of}\:{perpendicular} \\ $$$${tangents}\:{to}\:{an}\:{ellipse}\:{is}\:{another} \\ $$$${ellipse}. \\ $$

Question Number 81467    Answers: 1   Comments: 1

Question Number 81458    Answers: 0   Comments: 2

if a_1 = 3 ,a_2 =2 a_(n+2) = a_(n+1) +(a_1 /2) find a_6 =? mister W method a_n =A(((1+(√3))/2))^n +B(((1−(√3))/2))^n a_1 = A(((1+(√3))/2))+B(((1−(√3))/2))=3 a_2 = A(((1+(√3))/2))^2 +B(((1−(√3))/2))^2 =2 ⇒A+B+(A−B)(√3) =6 ⇒2(A+B)+(A−B)(√3) =4 A= ((4−(√3))/(√3)) , B = ((−4−(√3))/3) a_n = (((4−(√3))/(√3)))(((1+(√3))/2))^n −(((4+(√3))/(√3)))(((1−(√3))/2))^n

$$\mathrm{if}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{3}\:,\mathrm{a}_{\mathrm{2}} =\mathrm{2} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} +\frac{\mathrm{a}_{\mathrm{1}} }{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{6}} \:=? \\ $$$$\mathrm{mister}\:\mathrm{W}\:\mathrm{method} \\ $$$$\mathrm{a}_{\mathrm{n}} \:=\mathrm{A}\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{n}} +\mathrm{B}\left(\frac{\mathrm{1}−\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{n}} \\ $$$$\mathrm{a}_{\mathrm{1}} =\:\mathrm{A}\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\right)+\mathrm{B}\left(\frac{\mathrm{1}−\sqrt{\mathrm{3}}}{\mathrm{2}}\right)=\mathrm{3} \\ $$$$\mathrm{a}_{\mathrm{2}} \:=\:\mathrm{A}\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{B}\left(\frac{\mathrm{1}−\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{2} \\ $$$$\Rightarrow\mathrm{A}+\mathrm{B}+\left(\mathrm{A}−\mathrm{B}\right)\sqrt{\mathrm{3}}\:=\mathrm{6} \\ $$$$\Rightarrow\mathrm{2}\left(\mathrm{A}+\mathrm{B}\right)+\left(\mathrm{A}−\mathrm{B}\right)\sqrt{\mathrm{3}}\:=\mathrm{4} \\ $$$$\mathrm{A}=\:\frac{\mathrm{4}−\sqrt{\mathrm{3}}}{\sqrt{\mathrm{3}}}\:,\:\mathrm{B}\:=\:\frac{−\mathrm{4}−\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$$\mathrm{a}_{\mathrm{n}} \:=\:\left(\frac{\mathrm{4}−\sqrt{\mathrm{3}}}{\sqrt{\mathrm{3}}}\right)\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{n}} −\left(\frac{\mathrm{4}+\sqrt{\mathrm{3}}}{\sqrt{\mathrm{3}}}\right)\left(\frac{\mathrm{1}−\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{n}} \\ $$

Question Number 81446    Answers: 0   Comments: 5

given a_1 = 2 , a_2 = 3 and a_(n+2) = a_(n+1) + (a_n /2) find a_n =?

$$\mathrm{given}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{2}\:,\:\mathrm{a}_{\mathrm{2}} \:=\:\mathrm{3}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\:\frac{\mathrm{a}_{\mathrm{n}} }{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \:=? \\ $$

Question Number 81445    Answers: 0   Comments: 0

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