rounded to three decimal places, find the average rate of change of the polar function r = f(θ) on the…

rounded to three decimal places, find the average rate of change of the polar function r = f(θ) on the interval -2π/3, 0, where f(θ) = 2cos(3/4θ). then fill in the sentence below. answer attempt 1 out of 3 average rate of change = because this is function, the average rate of change can best be thought of as between the two points.

rounded to three decimal places, find the average rate of change of the polar function r = f(θ) on the interval -2π/3, 0, where f(θ) = 2cos(3/4θ). then fill in the sentence below. answer attempt 1 out of 3 average rate of change = because this is function, the average rate of change can best be thought of as between the two points.

Answer

Explanation:

Step1: Definir la fórmula de tasa media de cambio

La tasa media de cambio de una función $y = f(x)$ en el intervalo $[a,b]$ es $\frac{f(b)-f(a)}{b - a}$. Para la función polar $r = f(\theta)$ en el intervalo $[-\frac{2\pi}{3},0]$, tendremos $\frac{f(0)-f(-\frac{2\pi}{3})}{0-(-\frac{2\pi}{3})}$.

Step2: Calcular $f(0)$

Sustituir $\theta = 0$ en $f(\theta)=2\cos(\frac{3}{4}\theta)$. Entonces $f(0)=2\cos(0)=2\times1 = 2$.

Step3: Calcular $f(-\frac{2\pi}{3})$

Sustituir $\theta=-\frac{2\pi}{3}$ en $f(\theta)=2\cos(\frac{3}{4}\theta)$. Tenemos $\frac{3}{4}\theta=\frac{3}{4}\times(-\frac{2\pi}{3})=-\frac{\pi}{2}$, y $f(-\frac{2\pi}{3})=2\cos(-\frac{\pi}{2})=2\times0 = 0$.

Step4: Calcular la tasa media de cambio

Sustituir $f(0) = 2$ y $f(-\frac{2\pi}{3})=0$ en la fórmula de la tasa media de cambio: $\frac{f(0)-f(-\frac{2\pi}{3})}{0-(-\frac{2\pi}{3})}=\frac{2 - 0}{\frac{2\pi}{3}}=\frac{2}{\frac{2\pi}{3}}=\frac{3}{\pi}\approx0.955$.

Answer:

$0.955$