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Question Number 185518    Answers: 0   Comments: 1

Find the radius of convergence of Σ_(n=1) ^∞ ne^(−n^2 ) M.m

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{convergence}\:\mathrm{of} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{ne}^{−\mathrm{n}^{\mathrm{2}} } \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185517    Answers: 1   Comments: 0

Question Number 185470    Answers: 0   Comments: 3

Determine whether the series U_n =((1+2n^2 )/(1+n^2 )) is convergent or not M.m

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{U}_{\mathrm{n}} =\frac{\mathrm{1}+\mathrm{2n}^{\mathrm{2}} }{\mathrm{1}+\mathrm{n}^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{not} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185450    Answers: 0   Comments: 1

Write down the expansion of (a) cosx (b) (1/(l+x)), and hence show that ((cosx)/(1+x)) = 1−x+(x^2 /2)−(x^3 /2)+((13x^4 )/(24))+... M.m

$$\mathrm{Write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{cosx}\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{l}+\mathrm{x}},\:\mathrm{and}\:\mathrm{hence}\:\mathrm{show} \\ $$$$\mathrm{that}\:\frac{\mathrm{cosx}}{\mathrm{1}+\mathrm{x}}\:=\:\mathrm{1}−\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{13x}^{\mathrm{4}} }{\mathrm{24}}+... \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185449    Answers: 1   Comments: 0

Find the first four terms in the expansion of ((x−3)/((1−x^2 )^2 (2+x^2 ))) in ascending power of x. M.m

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\frac{\mathrm{x}−\mathrm{3}}{\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{2}+\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{in} \\ $$$$\mathrm{ascending}\:\mathrm{power}\:\mathrm{of}\:\mathrm{x}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185401    Answers: 0   Comments: 1

Show that ((1+z)/(1−z)) + ((1+z^ )/(1−z^ )) = ((2(1−∣z∣^2 ))/(∣1−z∣^2 )) Where z is a complex number Help!

$$\mathrm{Show}\:\mathrm{that}\:\frac{\mathrm{1}+\mathrm{z}}{\mathrm{1}−\mathrm{z}}\:+\:\frac{\mathrm{1}+\bar {\mathrm{z}}}{\mathrm{1}−\bar {\mathrm{z}}}\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mid\mathrm{z}\mid^{\mathrm{2}} \right)}{\mid\mathrm{1}−\mathrm{z}\mid^{\mathrm{2}} } \\ $$$$\mathrm{Where}\:\mathrm{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 185374    Answers: 1   Comments: 0

lim_(z→∞) ((iz^3 +iz−1)/((2z+3i)(z−i)^2 )) M.m

$$\mathrm{li}\underset{\mathrm{z}\rightarrow\infty} {\mathrm{m}}\frac{\mathrm{iz}^{\mathrm{3}} +\mathrm{iz}−\mathrm{1}}{\left(\mathrm{2z}+\mathrm{3i}\right)\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 185371    Answers: 1   Comments: 0

(1−z)(1−z^− ) = ? Where z is the complex number .

$$\left(\mathrm{1}−\mathrm{z}\right)\left(\mathrm{1}−\overset{−} {\mathrm{z}}\right)\:=\:? \\ $$$$\mathrm{Where}\:\mathrm{z}\:\mathrm{is}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number} \\ $$$$ \\ $$$$. \\ $$

Question Number 185278    Answers: 1   Comments: 3

Show that f(z)=z^2 is harmonic in polar form

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{harmonic}\:\mathrm{in} \\ $$$$\mathrm{polar}\:\mathrm{form} \\ $$

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!

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

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