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Question Number 185245 Answers: 1 Comments: 1

Show that f(z)=z^2 is uniformly continous in the region ∣z∣<R where 0<R<∞. Help!

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{uniformly} \\ $$$$\mathrm{continous}\:\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mid\mathrm{z}\mid<\mathrm{R} \\ $$$$\mathrm{where}\:\mathrm{0}<\mathrm{R}<\infty. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

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 185181 Answers: 2 Comments: 3

Question Number 185038 Answers: 1 Comments: 0

Find the range of values of x for which the series (x/(27))+(x^2 /(125))+...+(x^n /((2n+1)^3 ))+... is absolutely convergent. Help!

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{for}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{series}\:\frac{\mathrm{x}}{\mathrm{27}}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{125}}+...+\frac{\mathrm{x}^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{3}} }+... \\ $$$$\mathrm{is}\:\mathrm{absolutely}\:\mathrm{convergent}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 185036 Answers: 1 Comments: 0

Find the series for cosx. Hence, deduce series sin^2 x and show that, if x is small, ((sin^2 x−x^2 cosx)/x^4 )=(1/6)+(x^2 /(360)) approximately. Help!

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{series}\:\mathrm{for}\:\mathrm{cosx}.\:\mathrm{Hence},\: \\ $$$$\mathrm{deduce}\:\mathrm{series}\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}, \\ $$$$\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small},\:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{x}−\mathrm{x}^{\mathrm{2}} \mathrm{cosx}}{\mathrm{x}^{\mathrm{4}} }=\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{360}} \\ $$$$\mathrm{approximately}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 185014 Answers: 1 Comments: 1

The relation y=x^2 +kx+c, where K and C are constant passes through the points (−1, −2) and (1, 8) in the coordinate axes. calculate the value of C and K. M.m

$$\mathrm{The}\:\mathrm{relation}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} +\mathrm{kx}+\mathrm{c},\:\mathrm{where}\:\mathrm{K} \\ $$$$\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{constant}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{1},\:−\mathrm{2}\right)\:\mathrm{and}\:\left(\mathrm{1},\:\mathrm{8}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{coordinate}\:\mathrm{axes}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{C}\:\mathrm{and}\:\mathrm{K}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185116 Answers: 1 Comments: 0

Question Number 184959 Answers: 2 Comments: 0

Question Number 184939 Answers: 1 Comments: 0

What′s the convergent equation of this series? x_1 ^2 +x_2 ^2 +x_3 ^2 +...+x_n ^2 Help!

$$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{convergent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{series}? \\ $$$$\mathrm{x}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{3}} ^{\mathrm{2}} +...+\mathrm{x}_{\mathrm{n}} ^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184920 Answers: 1 Comments: 0

Investigate the series (1/(1×2))+(1/(2×3))+(1/(3×4))+(1/(4×5))+... Does it Converges or Diverges?

$$\mathrm{Investigate}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}}+... \\ $$$$\mathrm{Does}\:\mathrm{it}\:\mathrm{Converges}\:\mathrm{or}\:\mathrm{Diverges}? \\ $$

Question Number 184918 Answers: 2 Comments: 2

Show that 1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+... is not convergent Hi

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{6}}+...\:\mathrm{is}\: \\ $$$$\mathrm{not}\:\mathrm{convergent} \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$

Question Number 184915 Answers: 0 Comments: 2

Consider the series below 1+5+25+125+... Investigate whether it is convergent or divergent. Thanks

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below} \\ $$$$\mathrm{1}+\mathrm{5}+\mathrm{25}+\mathrm{125}+...\:\mathrm{Investigate} \\ $$$$\mathrm{whether}\:\mathrm{it}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\: \\ $$$$\mathrm{divergent}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$

Question Number 184873 Answers: 1 Comments: 0

Find the real number satisfying x=(√(1+(√(1+(√(1+x))))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number}\:\mathrm{satisfying} \\ $$$$\:\mathrm{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}}}} \\ $$

Question Number 184832 Answers: 4 Comments: 1

Given the acceleration a=−4sin2t, initial velocity v(0)=2, and the initial position of the body as s(0)=−3, find the body′s position at time t. Hi

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{acceleration}\: \\ $$$$\mathrm{a}=−\mathrm{4sin2t},\:\mathrm{initial}\:\mathrm{velocity}\: \\ $$$$\mathrm{v}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{and}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{position}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{as}\:\mathrm{s}\left(\mathrm{0}\right)=−\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{body}'\mathrm{s}\:\mathrm{position}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}. \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$

Question Number 184787 Answers: 0 Comments: 2

x^4 +16x^3 +9x^2 +256x+256=0 Find the values of x?

$$\mathrm{x}^{\mathrm{4}} +\mathrm{16x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{256x}+\mathrm{256}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}? \\ $$

Question Number 184744 Answers: 1 Comments: 1

given that the 5th term of an AP is more than its firs term by 12. and the 6th term is more than the first term by 10. find the fist term? common difference and 100th term

$${given}\:{that}\:{the}\:\mathrm{5}{th}\:{term}\:{of}\:{an}\:{AP}\:{is}\:{more}\:{than}\:{its}\:{firs}\:{term}\:{by}\:\mathrm{12}.\:{and}\:{the}\:\mathrm{6}{th}\:{term}\:{is}\:{more}\:{than}\:{the}\:{first}\:{term}\:{by}\:\mathrm{10}.\:{find}\:{the}\:{fist}\:{term}?\:{common}\:{difference}\:{and}\:\mathrm{100}{th}\:{term} \\ $$$$ \\ $$

Question Number 184731 Answers: 1 Comments: 0

Express this function in both its Cartesian and polar form f(z) = ze^(iz) . Help!

$$\mathrm{Express}\:\mathrm{this}\:\mathrm{function}\:\mathrm{in}\:\mathrm{both}\:\mathrm{its} \\ $$$$\mathrm{Cartesian}\:\mathrm{and}\:\mathrm{polar}\:\mathrm{form} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)\:=\:\mathrm{ze}^{\mathrm{iz}} . \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184656 Answers: 1 Comments: 0

prove that the area of a triangle whose two sides are A^− and B^− is given by (1/2)∣A×B∣. Also find the direction−cosine of normal to this area. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{are}\:\overset{−} {\mathrm{A}}\:\mathrm{and}\:\overset{−} {\mathrm{B}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{A}×\mathrm{B}\mid. \\ $$$$\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{direction}−\mathrm{cosine} \\ $$$$\mathrm{of}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{this}\:\mathrm{area}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184655 Answers: 1 Comments: 0

prove that an angle inscribe in a semi−circle is a right angle. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{inscribe}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{semi}−\mathrm{circle}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184574 Answers: 0 Comments: 5

Test whether this is Convergent or Divergent Σ_(n=0) ^∞ (−1)^n ((n!x^n )/(5n)) Help!

$$\mathrm{Test}\:\mathrm{whether}\:\mathrm{this}\:\mathrm{is}\:\mathrm{Convergent}\:\mathrm{or} \\ $$$$\mathrm{Divergent} \\ $$$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{n}!\mathrm{x}^{\mathrm{n}} }{\mathrm{5n}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184497 Answers: 1 Comments: 0

Question Number 184487 Answers: 0 Comments: 1

Question Number 184454 Answers: 0 Comments: 1

Question Number 184320 Answers: 0 Comments: 4

All-time Universal Formula determinant (((OLD+1=NEW))) Year:-The above formula applies every year. Month:-It also applies every month. Day:-It also applies every day. .... Second:-It also applies every second. ... SO, along with Happy New Year! also: Happy New Month! Happy New Day! .... Happy New Second! ...

Question Number 184311 Answers: 1 Comments: 0

Question Number 184307 Answers: 1 Comments: 0

Show that the boundary−value problem y′′+λy=0 y(0)=0, y(L)=0 has only the trival solution y=0 for the cases λ=0 and λ<0. let L be a non−zero real number. ?

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{boundary}−\mathrm{value} \\ $$$$\mathrm{problem}\:\mathrm{y}''+\lambda\mathrm{y}=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}, \\ $$$$\mathrm{y}\left(\mathrm{L}\right)=\mathrm{0}\:\mathrm{has}\:\mathrm{only}\:\mathrm{the}\:\mathrm{trival}\:\mathrm{solution} \\ $$$$\mathrm{y}=\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{cases}\:\lambda=\mathrm{0}\:\mathrm{and}\:\lambda<\mathrm{0}. \\ $$$$\mathrm{let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{zero}\:\mathrm{real}\:\mathrm{number}. \\ $$$$ \\ $$$$ \\ $$$$? \\ $$

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