Question and Answers Forum

given that g(x) = { ((x + 2 , if 0 ≤ x < 2)),((x^2 , if 2 ≤ x < 4)) :} is periodic of period 4. sketch the curve for g(x) in the interval 0≤ x < 8 evaluate g(−6).

$$\mathrm{given}\:\:\mathrm{that} \\ $$$$\:\mathrm{g}\left({x}\right)\:=\:\begin{cases}{{x}\:+\:\mathrm{2}\:,\:\mathrm{if}\:\:\mathrm{0}\:\leqslant\:{x}\:<\:\mathrm{2}}\\{{x}^{\mathrm{2}} \:,\:\mathrm{if}\:\:\mathrm{2}\:\leqslant\:{x}\:<\:\mathrm{4}}\end{cases} \\ $$$$\mathrm{is}\:\mathrm{periodic}\:\mathrm{of}\:\mathrm{period}\:\mathrm{4}.\: \\ $$$$\mathrm{sketch}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{for}\:\mathrm{g}\left({x}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\:\:\mathrm{0}\leqslant\:{x}\:<\:\mathrm{8} \\ $$$$\mathrm{evaluate}\:\:\mathrm{g}\left(−\mathrm{6}\right). \\ $$

Question Number 84109 Answers: 1 Comments: 2

Question Number 84106 Answers: 0 Comments: 1

∫ (x^4 /(√(1−x^4 ))) dx = ?

$$\int\:\frac{\mathrm{x}^{\mathrm{4}} }{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$

Question Number 84101 Answers: 2 Comments: 0

Find the reduction formula ∫x^n e^(ax) dx

$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{reduction}}\:\boldsymbol{\mathrm{formula}} \\ $$$$\:\:\int\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{ax}}} \:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 84100 Answers: 2 Comments: 0

Find the differential equations: x(dy/dx)= y− (√(x^2 +y^2 ))

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equations}: \\ $$$$\:\:\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}=\:\mathrm{y}−\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$

Question Number 84087 Answers: 0 Comments: 1

∫_0 ^3 (√(1+sinh^2 t)) dt

$$\int_{\mathrm{0}} ^{\mathrm{3}} \sqrt{\mathrm{1}+{sinh}^{\mathrm{2}} {t}}\:{dt} \\ $$

Question Number 84085 Answers: 1 Comments: 0

solve (d/dr)(r(dθ/dr))=0

$${solve} \\ $$$$\frac{{d}}{{dr}}\left({r}\frac{{d}\theta}{{dr}}\right)=\mathrm{0} \\ $$

Question Number 84083 Answers: 1 Comments: 3

lim_(a→x) ((((√x) −(√a) −(√(x−a ))))/(√(x^2 −a^2 ))) =

$$\underset{\mathrm{a}\rightarrow\mathrm{x}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{x}}\:−\sqrt{\mathrm{a}}\:−\sqrt{\mathrm{x}−\mathrm{a}\:}\right)}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}\:= \\ $$

Question Number 84117 Answers: 2 Comments: 0

Question Number 84068 Answers: 0 Comments: 4

Question Number 84067 Answers: 3 Comments: 0

If lx+my=1 touches the curve (ax)^n +(by)^n =1, show that ((l/a))^(n/(n−1)) +((m/b))^(n/(n−1)) =1.

$$\:\mathrm{If}\:\boldsymbol{{lx}}+\boldsymbol{{my}}=\mathrm{1}\:\mathrm{touches}\:\mathrm{the}\:\mathrm{curve}\:\left(\boldsymbol{\mathrm{ax}}\right)^{\boldsymbol{\mathrm{n}}} +\left(\boldsymbol{\mathrm{by}}\right)^{\boldsymbol{\mathrm{n}}} =\mathrm{1},\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\left(\frac{\boldsymbol{{l}}}{\boldsymbol{{a}}}\right)^{\frac{\boldsymbol{{n}}}{\boldsymbol{{n}}−\mathrm{1}}} +\left(\frac{\boldsymbol{{m}}}{\boldsymbol{{b}}}\right)^{\frac{\boldsymbol{{n}}}{\boldsymbol{{n}}−\mathrm{1}}} =\mathrm{1}. \\ $$

Question Number 84065 Answers: 1 Comments: 2

Determine a and b in order that _(x→0) ^(lim) ((x(1+a cos x)−b sin x )/x^3 )=1.

Question Number 84063 Answers: 0 Comments: 0

Find the value of 𝛉 in the Mean Value Theorem f(x+h)=f(x)+h f^( ′) (x+𝛉h) if f(x)= (1/x).

Question Number 84059 Answers: 1 Comments: 2

Find (dy/dx) of x^m x^n =(x+y)^(m+n) .

$$ \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{of}}\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{m}}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \:=\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)^{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} . \\ $$

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