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Question Number 113552    Answers: 1   Comments: 0

Question Number 113549    Answers: 0   Comments: 0

let A = (((1 −(1/n))),(((1/n) 1)) ) 1) calculate A^2 2) calculate A^m (m integr natural) 3) coclude A^n and lim_(n→+∞) A^n 4) calculate e^A and e^(−A)

$$\mathrm{let}\:\mathrm{A}\:\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\frac{\mathrm{1}}{\mathrm{n}}}\\{\frac{\mathrm{1}}{\mathrm{n}}\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\:\mathrm{A}^{\mathrm{m}} \:\:\:\:\:\left(\mathrm{m}\:\:\mathrm{integr}\:\mathrm{natural}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{coclude}\:\mathrm{A}^{\mathrm{n}} \:\:\:\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \\ $$

Question Number 113542    Answers: 0   Comments: 2

App Update v2.203 A function plotter for one variable is available. Steps to use Insert Drawing Insert Equation select equation from the list of shape tap on BUILD and select plot A sample plot is show as image below. Line color for plot can be changed using edit shape menu to change range of x values select scale from options menu. to zoomin/out use option menu to scroll with zoom: clear selection and place touch in move mode. You can add multiple plots on one drawing and also add another drawing on the canvas.

$$\mathrm{App}\:\mathrm{Update}\:\mathrm{v2}.\mathrm{203} \\ $$$$\mathrm{A}\:\mathrm{function}\:\mathrm{plotter}\:\mathrm{for}\:\mathrm{one}\:\mathrm{variable} \\ $$$$\mathrm{is}\:\mathrm{available}.\:\mathrm{Steps}\:\mathrm{to}\:\mathrm{use} \\ $$$$\mathrm{Insert}\:\mathrm{Drawing} \\ $$$$\mathrm{Insert}\:\mathrm{Equation} \\ $$$$\mathrm{select}\:\mathrm{equation}\:\mathrm{from}\:\mathrm{the}\:\mathrm{list}\:\mathrm{of}\:\mathrm{shape} \\ $$$$\mathrm{tap}\:\mathrm{on}\:\mathrm{BUILD}\:\:\mathrm{and}\:\mathrm{select}\:\mathrm{plot} \\ $$$$\mathrm{A}\:\mathrm{sample}\:\mathrm{plot}\:\mathrm{is}\:\mathrm{show}\:\mathrm{as}\:\mathrm{image}\:\mathrm{below}. \\ $$$$\mathrm{Line}\:\mathrm{color}\:\mathrm{for}\:\mathrm{plot}\:\mathrm{can}\:\mathrm{be}\:\mathrm{changed} \\ $$$$\mathrm{using}\:\mathrm{edit}\:\mathrm{shape}\:\mathrm{menu} \\ $$$$\mathrm{to}\:\mathrm{change}\:\mathrm{range}\:\mathrm{of}\:\mathrm{x}\:\mathrm{values}\:\mathrm{select} \\ $$$$\mathrm{scale}\:\mathrm{from}\:\mathrm{options}\:\mathrm{menu}. \\ $$$$\mathrm{to}\:\mathrm{zoomin}/\mathrm{out}\:\mathrm{use}\:\mathrm{option}\:\mathrm{menu} \\ $$$$\mathrm{to}\:\mathrm{scroll}\:\mathrm{with}\:\mathrm{zoom}:\:\mathrm{clear}\:\mathrm{selection}\:\mathrm{and} \\ $$$$\mathrm{place}\:\mathrm{touch}\:\mathrm{in}\:\mathrm{move}\:\mathrm{mode}. \\ $$$$\mathrm{You}\:\mathrm{can}\:\mathrm{add}\:\mathrm{multiple}\:\mathrm{plots}\:\mathrm{on} \\ $$$$\mathrm{one}\:\mathrm{drawing}\:\mathrm{and}\:\mathrm{also}\:\mathrm{add}\:\mathrm{another} \\ $$$$\mathrm{drawing}\:\mathrm{on}\:\mathrm{the}\:\mathrm{canvas}. \\ $$

Question Number 113532    Answers: 2   Comments: 1

Question Number 113530    Answers: 2   Comments: 0

Question Number 113524    Answers: 2   Comments: 0

Question Number 113511    Answers: 1   Comments: 0

Question Number 113510    Answers: 1   Comments: 0

Question Number 113508    Answers: 1   Comments: 2

Question Number 113507    Answers: 2   Comments: 0

Question Number 113505    Answers: 1   Comments: 0

Question Number 113504    Answers: 0   Comments: 3

Question Number 113503    Answers: 0   Comments: 1

Question Number 113499    Answers: 0   Comments: 0

Question Number 113490    Answers: 0   Comments: 1

Question Number 113488    Answers: 2   Comments: 0

prove that ((sin(2a)cos(2a))/(cos(4a))) = (1/2) tan(4a)

$${prove}\:{that} \\ $$$$\frac{{sin}\left(\mathrm{2}{a}\right){cos}\left(\mathrm{2}{a}\right)}{{cos}\left(\mathrm{4}{a}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{tan}\left(\mathrm{4}{a}\right) \\ $$

Question Number 113486    Answers: 1   Comments: 1

Question Number 113472    Answers: 1   Comments: 0

Question Number 113468    Answers: 0   Comments: 0

Question Number 113465    Answers: 0   Comments: 7

Question Number 113464    Answers: 1   Comments: 0

(x^2 (d^2 y/dx^2 ) +x (dy/dx) + 1).y = 0

$$\:\left({x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+{x}\:\frac{{dy}}{{dx}}\:+\:\mathrm{1}\right).{y}\:=\:\mathrm{0} \\ $$

Question Number 113456    Answers: 0   Comments: 0

Question Number 113455    Answers: 1   Comments: 1

Question Number 113452    Answers: 1   Comments: 0

Question Number 113451    Answers: 3   Comments: 0

If 2x=a^n +a^(−n) and 2y=a^n −a^(−n) calculate the value of x^2 −y^(2 ) in its simplest form

$$\mathrm{If}\:\mathrm{2x}=\mathrm{a}^{\mathrm{n}} +\mathrm{a}^{−\mathrm{n}} \:\mathrm{and}\:\mathrm{2y}=\mathrm{a}^{\mathrm{n}} −\mathrm{a}^{−\mathrm{n}} \:\mathrm{calculate} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}\:} \:\mathrm{in}\:\mathrm{its}\:\mathrm{simplest}\:\mathrm{form} \\ $$

Question Number 113444    Answers: 1   Comments: 0

y′′−2ay′+(1+a^2 )y=te^(at) +sint

$$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$

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