- #1
anonymous12
- 29
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Homework Statement
For the function f(x) = 3sin 2x, find the instantaneous rate of change at point A [itex](\frac{\pi}{6}, f(\frac{\pi}{6}))[/itex]
Homework Equations
iroc = instantaneous rate of change
[tex]iroc= \lim_{h\to 0} \frac{f(a+h) - f(a)}{h}[/tex]
The Attempt at a Solution
iroc = instantaneous rate of change
[tex]iroc= \lim_{h\to 0} \frac{(3sin2(\frac{\pi}{6}+0.001)) - (3sin2(\frac{\pi}{6})}{0.001}[/tex]
[tex]iroc= \lim_{h\to 0} \frac{(3sin(\frac{\pi}{3}+0.002)) - (3sin(\frac{\pi}{3}))}{0.001}[/tex]
[tex]iroc= \lim_{h\to 0} \frac{(3(\frac{\sqrt3}{2}+0.002)) - (3(\frac{\sqrt{3}}{2}))}{0.001}[/tex]
[tex]iroc= \lim_{h\to 0} \frac{(3(\frac{\sqrt3 + 0.004}{2})) - (\frac{3\cdot\sqrt{3}}{2}))}{0.001}[/tex]
[tex]iroc= \lim_{h\to 0} \frac{(\frac{3\sqrt3 + 0.012}{2})) - (\frac{3\sqrt{3}}{2}))}{0.001}[/tex]
[tex]iroc = 6[/tex]
Is this answer correct?