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Question Number 185243    Answers: 1   Comments: 3

Using ε−δ approach prove that lim_(z→i) ((3z^4 −2z^3 +8z^2 −2z+5)/(z−i))=4+4i Help!

$$\mathrm{Using}\:\varepsilon−\delta\:\mathrm{approach}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{li}\underset{\mathrm{z}\rightarrow\mathrm{i}} {\mathrm{m}}\frac{\mathrm{3z}^{\mathrm{4}} −\mathrm{2z}^{\mathrm{3}} +\mathrm{8z}^{\mathrm{2}} −\mathrm{2z}+\mathrm{5}}{\mathrm{z}−\mathrm{i}}=\mathrm{4}+\mathrm{4i} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 185239    Answers: 0   Comments: 3

Question Number 185236    Answers: 0   Comments: 1

Question Number 185231    Answers: 3   Comments: 0

Question Number 185229    Answers: 1   Comments: 0

Question Number 185224    Answers: 2   Comments: 0

Question Number 185222    Answers: 2   Comments: 0

A ball falls from a height of 10m and lands on the ground 75% of each time it falls, it gets up again; of the What is the total distance traveled by the ball? (a) 35m b) 40m c) 70m d) 75m

$$ \\ $$A ball falls from a height of 10m and lands on the ground 75% of each time it falls, it gets up again; of the What is the total distance traveled by the ball? (a) 35m b) 40m c) 70m d) 75m

Question Number 185213    Answers: 0   Comments: 0

Question Number 185212    Answers: 0   Comments: 0

Question Number 185211    Answers: 3   Comments: 0

Question Number 185210    Answers: 3   Comments: 2

x=((x^2 +1)/(α+1)) x=?

$${x}=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\alpha+\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$

Question Number 185209    Answers: 2   Comments: 0

Question Number 185206    Answers: 0   Comments: 1

Question Number 185204    Answers: 1   Comments: 1

1+(1/(2+(1/(3+(1/(4+(1/⋱)))))))=???

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+\frac{\mathrm{1}}{\ddots}}}}=??? \\ $$

Question Number 185203    Answers: 2   Comments: 0

Question Number 185198    Answers: 0   Comments: 2

Question Number 185192    Answers: 0   Comments: 2

Question Number 185191    Answers: 1   Comments: 0

y = sin (1/x) ⇒ y^′ = ?

$$\mathrm{y}\:=\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\Rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 185190    Answers: 0   Comments: 0

Question Number 185181    Answers: 2   Comments: 3

Question Number 185180    Answers: 1   Comments: 0

Question Number 185178    Answers: 3   Comments: 1

Question Number 185169    Answers: 1   Comments: 1

calcul de l′ angle x △ABD ((sin y)/(AD))=((sin44 )/(BD)) (1) △ADC ((sin x)/(AD))=((sin48 )/(DC)) (2) (1) BD sin y=ADsin 44 (2) DCsinx =ADsin 48 (((1))/((2)))⇔ ((BDsin y)/(DCsin x))=((sin 44)/(sin 48)) (3) △BDC ((sin 14)/(BD))=((sin 28)/(DC)) ((BD)/(DC))=((sin 14)/(sin 28)) (3)⇔((sin 14×)/(sin 28×))((sin y)/(sin x))=((sin 44)/(sin 48)) Relation entre x et y △ABC (∡A +∡B+ ∡C)=180 48+44+y+28+14+x=180 x+y=46 ⇒ y=46−x ((sin x)/(sin y))=((sin 48×sin 28)/(sin 44×sin 14)) ((sinx)/(sin(46−x)))=((2sin 48×cos 14)/(sin 44)) =((sin x)/(sin 46cos x−cos 46sin x)) =((sin x)/(cos x(sin 46−tan x×cos 46))) =((tan x)/(sin 46−cos 46×tan x)) sin 44×tan x=2sin 48×cos 14(sin 46−cos 46tan x) (sin 44+2sin 48cos 14×cos 46)tan x= 2sin 48cos 14×sin 46 tan x=((2sin 48×cos 14×sin 46)/(sin 44+2sin 48×cos 14×cos 46)) sin 44= sin 48= sin 46 cos 14= cos 46= tan x=0,61150462 soit: X=31,446^°

$${calcul}\:{de}\:{l}'\:{angle}\:\boldsymbol{{x}} \\ $$$$\bigtriangleup{ABD}\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{y}}{\mathrm{AD}}=\frac{\mathrm{sin44}\:}{\mathrm{BD}}\:\:\left(\mathrm{1}\right) \\ $$$$\bigtriangleup{ADC}\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{AD}}=\frac{\mathrm{sin48}\:}{\mathrm{DC}}\:\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\mathrm{BD}\:\mathrm{sin}\:\mathrm{y}=\mathrm{ADsin}\:\mathrm{44} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\mathrm{DCsinx}\:=\mathrm{ADsin}\:\mathrm{48} \\ $$$$ \\ $$$$\frac{\left(\mathrm{1}\right)}{\left(\mathrm{2}\right)}\Leftrightarrow\:\frac{\mathrm{BDsin}\:\mathrm{y}}{\mathrm{DCsin}\:\mathrm{x}}=\frac{\mathrm{sin}\:\mathrm{44}}{\mathrm{sin}\:\mathrm{48}}\:\:\:\left(\mathrm{3}\right) \\ $$$$ \\ $$$$\bigtriangleup{BDC}\:\:\:\:\frac{\mathrm{sin}\:\mathrm{14}}{\mathrm{BD}}=\frac{\mathrm{sin}\:\mathrm{28}}{\mathrm{DC}} \\ $$$$\:\:\:\:\:\frac{\mathrm{BD}}{\mathrm{DC}}=\frac{\mathrm{sin}\:\mathrm{14}}{\mathrm{sin}\:\mathrm{28}} \\ $$$$\left(\mathrm{3}\right)\Leftrightarrow\frac{\mathrm{sin}\:\mathrm{14}×}{\mathrm{sin}\:\mathrm{28}×}\frac{\mathrm{sin}\:\mathrm{y}}{\mathrm{sin}\:\mathrm{x}}=\frac{\mathrm{sin}\:\mathrm{44}}{\mathrm{sin}\:\mathrm{48}}\: \\ $$$${Relation}\:{entre}\:\boldsymbol{{x}}\:{et}\:\:\boldsymbol{{y}} \\ $$$$\bigtriangleup{ABC}\:\:\:\:\left(\measuredangle{A}\:\:+\measuredangle{B}+\:\:\measuredangle{C}\right)=\mathrm{180} \\ $$$$\:\mathrm{48}+\mathrm{44}+{y}+\mathrm{28}+\mathrm{14}+{x}=\mathrm{180} \\ $$$${x}+{y}=\mathrm{46}\:\Rightarrow\:\:\:\:{y}=\mathrm{46}−{x} \\ $$$$\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{y}}=\frac{\mathrm{sin}\:\mathrm{48}×\mathrm{sin}\:\mathrm{28}}{\mathrm{sin}\:\mathrm{44}×\mathrm{sin}\:\mathrm{14}} \\ $$$$\frac{\mathrm{sinx}}{\mathrm{sin}\left(\mathrm{46}−\mathrm{x}\right)}=\frac{\mathrm{2sin}\:\mathrm{48}×\mathrm{cos}\:\mathrm{14}}{\mathrm{sin}\:\mathrm{44}} \\ $$$$=\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{46cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{46sin}\:\mathrm{x}} \\ $$$$=\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}\left(\mathrm{sin}\:\mathrm{46}−\mathrm{tan}\:\mathrm{x}×\mathrm{cos}\:\mathrm{46}\right)} \\ $$$$=\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{46}−\mathrm{cos}\:\mathrm{46}×\mathrm{tan}\:\mathrm{x}} \\ $$$$\mathrm{sin}\:\mathrm{44}×\mathrm{tan}\:\mathrm{x}=\mathrm{2sin}\:\mathrm{48}×\mathrm{cos}\:\mathrm{14}\left(\mathrm{sin}\:\mathrm{46}−\mathrm{cos}\:\mathrm{46tan}\:\mathrm{x}\right) \\ $$$$\left(\mathrm{sin}\:\mathrm{44}+\mathrm{2sin}\:\mathrm{48cos}\:\mathrm{14}×\mathrm{cos}\:\mathrm{46}\right)\mathrm{tan}\:\mathrm{x}= \\ $$$$\mathrm{2sin}\:\mathrm{48cos}\:\mathrm{14}×\mathrm{sin}\:\mathrm{46} \\ $$$$ \\ $$$$\:\:\mathrm{tan}\:\mathrm{x}=\frac{\mathrm{2sin}\:\mathrm{48}×\mathrm{cos}\:\mathrm{14}×\mathrm{sin}\:\:\mathrm{46}}{\mathrm{sin}\:\mathrm{44}+\mathrm{2sin}\:\mathrm{48}×\mathrm{cos}\:\mathrm{14}×\mathrm{cos}\:\mathrm{46}} \\ $$$$\mathrm{sin}\:\mathrm{44}=\:\:\:\mathrm{sin}\:\mathrm{48}=\:\:\:\mathrm{sin}\:\mathrm{46} \\ $$$$\mathrm{cos}\:\mathrm{14}=\:\:\:\:\mathrm{cos}\:\mathrm{46}=\:\:\:\:\: \\ $$$$\mathrm{tan}\:\boldsymbol{\mathrm{x}}=\mathrm{0},\mathrm{61150462} \\ $$$$ \\ $$$${soit}:\:\:\:\:\:\boldsymbol{\mathrm{X}}=\mathrm{31},\mathrm{446}^{°} \:\: \\ $$$$ \\ $$

Question Number 185167    Answers: 1   Comments: 0

Question Number 185166    Answers: 1   Comments: 0

Question Number 185165    Answers: 1   Comments: 0

Simplify : ((i^(2022) +i^(2023) +i^(2024) +i^(2025) )/(1+i))

$$\mathrm{Simplify}\::\:\frac{\mathrm{i}^{\mathrm{2022}} +\mathrm{i}^{\mathrm{2023}} +\mathrm{i}^{\mathrm{2024}} +\mathrm{i}^{\mathrm{2025}} }{\mathrm{1}+\mathrm{i}} \\ $$

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