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# Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.$\displaystyle \lim_{\theta \to 0}\frac{\sin 3\theta}{\tan 2\theta}$

## \begin{aligned}&\text { For } f(\theta)=\frac{\sin 3 \theta}{\tan 2 \theta}\\&\begin{array}{|l|c|}\hline \theta & f(\theta) \\\hline\pm 0.1 & 1.457847 \\\pm 0.01 & 1.499575 \\\pm 0.001 & 1.499996 \\\pm 0.0001 & 1.500000 \\\hline\end{array}\end{aligned}It appears that $\lim _{\theta \rightarrow 0} \frac{\sin 3 \theta}{\tan 2 \theta}=1.5$The graph confirms that result.

Limits

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

So the question is human as and then make zero scientific upon to amputate. No, just can utterance. Three D. To 1 2012th Dinner. Mhm saying 40 to at one. And that is it off computer and let me was thrown from the humidity cameras for Yeah, We know that is limited data tends to zero sign detail upon detail physicals too. It just is not for me. So now they separate in me Detect tends to zero saying do you keep that 1 30 England here? I'm gonna be banned dividing back. Huh? No. All right. You pick up. Yeah. Sign Makita. Then we're going to teacher and they're they're great cost to the still as Detections to zero scientific about it happens to one saying to be delivered to the doors again stolen in this target counselor. So we are left with one. You do it three x 2 mm hmm one. And when you get into the call 00 lives. What? So this is the Koran strictly by the book at one point this is the answer. This can be cross checked with the graph of scientific done by saying. So the class of thank you that was in that end with is given by this here it is clearly visible at this point is 1.5 First from the graph at zero X zero again on the front side. So from the ground and by calculation and men so one hand is the correct answer. Yeah. Mhm

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#### Topics

Limits

Derivatives

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp