University of California, Berkeley

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Problem 18

Estimating a Limit Numerically In Exereises $11-18$ ,create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result.

$$\lim _{x \rightarrow 0} \frac{\tan x}{\tan 2 x}$$

Answer

$$\lim _{x \rightarrow 0}\left[\frac{\tan x}{\tan 2 x}\right]=0.5$$

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## Discussion

## Video Transcript

Okay, so we're off to create a table to find this limit value of X equals negative 0.1. You get tangents of making a 0.1 over 10 just two times negative 0.1, which is approximately why was moved for 2.49497 Now an X equals negative point till one with the wise approximately 0.49995 when X is equal to point negative point. So no one could get wise approximately quite for 99 99 no one except to point no, don't want. We get wise approximately important for 99 9 next week with the point you know, when we get wise, you could do for you point for 99 and then when x clinical 2.1, we get why people 2.49497 to see that the limited Exit 30 0 when it's approaching from the left, is approaching approximately 00.5. And when it's pushing from the right, it's approaching approximately point pipe. So we could say the limit as excuses go is approximately 0.5

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