1. ## Evaluating this limit....

Question: Evaluate limx->pi/3 sqrt[sin(5x/2)]

So by using direct substitution that would become sqrt[sin(2.618)].
sin(2.618) = 0.5
limit = sqrt(0.5)

This just feels wrong. Did I do the process incorrectly?
Any help is appreciated!

2. I don't see anything wrong with it, other than claiming certain decimals are equal when they're not. Your final answer is correct, and the overall logic is correct, but it's better to use exact numbers along the way when you can.

3. Also remember that $\displaystyle \sqrt{0.5} = \sqrt{\frac{1}{2}}$

$\displaystyle = \frac{\sqrt{1}}{\sqrt{2}}$

$\displaystyle = \frac{1}{\sqrt{2}}$

$\displaystyle = \frac{\sqrt{2}}{2}$.

4. Originally Posted by iluvmathbutitshard
Question: Evaluate limx->pi/3 sqrt[sin(5x/2)]

So by using direct substitution that would become sqrt[sin(2.618)].
sin(2.618) = 0.5
limit = sqrt(0.5)

This just feels wrong. Did I do the process incorrectly?
Any help is appreciated!
$\displaystyle \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi-\pi/6)}=\sqrt{\sin(\pi/6)}$

and $\displaystyle \pi/6$ is $\displaystyle 30^{\circ}$ so $\displaystyle \sin(\pi/6)=1/2$

CB

5. $\displaystyle \sqrt{\sin(5\pi/6)}=\sqrt{\sin(-\pi/6)}=\sqrt{\sin(\pi/6)}$
Not sure about that equality. I'd agree with this:

$\displaystyle \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi/6)},$ since the sin function is symmetric about $\displaystyle \pi/2.$

6. Originally Posted by Ackbeet
Not sure about that equality. I'd agree with this:

$\displaystyle \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi/6)},$ since the sin function is symmetric about $\displaystyle \pi/2.$
Fixed now

CB