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Question Number 187155 Answers: 2 Comments: 2

f(x)=x.e^(2x) =>f^((n)) (x)=

$${f}\left({x}\right)={x}.{e}^{\mathrm{2}{x}} \\ $$$$=>{f}^{\left({n}\right)} \left({x}\right)= \\ $$$$ \\ $$

Question Number 186962 Answers: 1 Comments: 0

Question Number 186662 Answers: 1 Comments: 0

Question Number 186636 Answers: 1 Comments: 2

x^2 +x+1=0 x^(92) =?

$${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:{x}^{\mathrm{92}} =? \\ $$

Question Number 186446 Answers: 0 Comments: 0

Question Number 186437 Answers: 1 Comments: 2

∫_0 ^( 1) (1/( (√(x(√(x^2 (√(x^3 (√(x^4 +1)))))))) )) dx

$$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 186230 Answers: 2 Comments: 0

Question Number 186080 Answers: 0 Comments: 0

Question Number 186077 Answers: 1 Comments: 0

Prove that ▽•(∅A^− )=(▽∅)•A+∅(▽•A^− ). Help!

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\bigtriangledown\bullet\left(\varnothing\overset{−} {\mathrm{A}}\right)=\left(\bigtriangledown\varnothing\right)\bullet\mathrm{A}+\varnothing\left(\bigtriangledown\bullet\overset{−} {\mathrm{A}}\right). \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 186074 Answers: 1 Comments: 0

Prove that div(curlA^− )=0 Help!

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{div}\left(\mathrm{curl}\overset{−} {\mathrm{A}}\right)=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 186026 Answers: 1 Comments: 0

Question Number 185996 Answers: 2 Comments: 0

Question Number 185900 Answers: 2 Comments: 0

Question Number 185847 Answers: 0 Comments: 0

Question Number 185786 Answers: 0 Comments: 0

Question Number 185781 Answers: 1 Comments: 0

Question Number 185553 Answers: 1 Comments: 0

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

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

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