[tex]\mathrm{La\:periodicidad\:de\:}a\cdot \\:sin\:\left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicidad\:de}\:\sin \left(x\right)}{|b|}[/tex]
[tex]\mathrm{La\:periodicidad\:de\:}\\:sin\:\left(x\right)\:\mathrm{es}\:2\pi[/tex]
[tex]=\frac{2\pi }{\left|3\right|}[/tex]
[tex]\mathrm{Simplificamos}[/tex]
[tex]=\frac{2\pi }{3}[/tex]
[tex]\mathrm{El\:dominio\:de\:}\:2\sin \left(3x+\pi \right)-1\::\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Notacion\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{El\:rango\:de\:}2\sin \left(3x+\pi \right)-1:\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-3\le \:f\left(x\right)\le \:1\:\\ \:\mathrm{Notacion\:intervalo}&\:\left[-3,\:1\right]\end{bmatrix}[/tex]
[tex]\mathrm{Puntos\:de\:interseccion\:con\:el\:eje\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{X\:intersecta}:\:\left(\frac{7\pi }{18}+\frac{2\pi n}{3},\:0\right),[/tex][tex]\left(\frac{11\pi }{18}+\frac{2\pi n}{3},\:0\right),\:\mathrm{Y\:intersecta}:\:\left(0,\:-1\right)[/tex]
[tex]\mathrm{Asintotas\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{Ninguno}[/tex]
[tex]\mathrm{Puntos\:extremos\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{Minimo}\left(\frac{\pi }{6}+\frac{2\pi }{3}n,\:-3\right),\:\mathrm{Maximo}\left(\frac{\pi }{2}+\frac{2\pi }{3}n,\:1\right)[/tex]Es la b)
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
[tex]\mathrm{La\:periodicidad\:de\:}a\cdot \\:sin\:\left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicidad\:de}\:\sin \left(x\right)}{|b|}[/tex]
[tex]\mathrm{La\:periodicidad\:de\:}\\:sin\:\left(x\right)\:\mathrm{es}\:2\pi[/tex]
[tex]=\frac{2\pi }{\left|3\right|}[/tex]
[tex]\mathrm{Simplificamos}[/tex]
[tex]=\frac{2\pi }{3}[/tex]
[tex]\mathrm{El\:dominio\:de\:}\:2\sin \left(3x+\pi \right)-1\::\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Notacion\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{El\:rango\:de\:}2\sin \left(3x+\pi \right)-1:\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-3\le \:f\left(x\right)\le \:1\:\\ \:\mathrm{Notacion\:intervalo}&\:\left[-3,\:1\right]\end{bmatrix}[/tex]
[tex]\mathrm{Puntos\:de\:interseccion\:con\:el\:eje\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{X\:intersecta}:\:\left(\frac{7\pi }{18}+\frac{2\pi n}{3},\:0\right),[/tex][tex]\left(\frac{11\pi }{18}+\frac{2\pi n}{3},\:0\right),\:\mathrm{Y\:intersecta}:\:\left(0,\:-1\right)[/tex]
[tex]\mathrm{Asintotas\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{Ninguno}[/tex]
[tex]\mathrm{Puntos\:extremos\:de}\:2\sin \left(3x+\pi \right)-1:\quad \mathrm{Minimo}\left(\frac{\pi }{6}+\frac{2\pi }{3}n,\:-3\right),\:\mathrm{Maximo}\left(\frac{\pi }{2}+\frac{2\pi }{3}n,\:1\right)[/tex]Es la b)