The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.
<h3>How to determine the instantaneous rate of change of a given function</h3>
The <em>instantaneous</em> rate of change at a given value of
can be found by concept of derivative, which is described below:
![g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D)
Where
is the <em>difference</em> rate.
In this question we must find an expression for the <em>instantaneous</em> rate of change of
if
and evaluate the resulting expression for
. Then, we have the following procedure below:
![g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Csin%20%28x%2Bh%29-%5Csin%20x%7D%7Bh%7D)
![g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Csin%20x%5Ccdot%20%5Ccos%20h%20%2B%5Csin%20h%5Ccdot%20%5Ccos%20x%20-%5Csin%20x%7D%7Bh%7D)
![g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Csin%20h%7D%7Bh%7D%5Ccdot%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Ccos%20x)
![g(x) = \cos x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Ccos%20x)
Now we evaluate
for
:
![g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}](https://tex.z-dn.net/?f=g%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B3%7D%20%5Cright%29%20%3D%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037
Answer:
45
40 percent (calculated percentage %) of what number equals 18? Answer: 45.
Answer: congruent segment
Step-by-step explanation: it is the same segment on a different radius of a circle
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