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Numerade Educator

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Problem 66 Hard Difficulty

Use the series in Example 13(b) to evaluate

$ \lim_ {x \to 0} \frac {\tan x - x}{x^3} $

We found this limit in Example 4.4.4 using 1' Hospital's Rule three times. Which method do you prefer?

Answer

$\frac{1}{3}$

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Video Transcript

use the serious, in example, her team party to be valid. So this limits. Okay, so lame. Ex too. It goes to zero tendon X minus X over. Execute. We can expand tender necks. I'm somebody. So it's going to be limb x zero. Explore s X cubed over three, plus some hair of the term of Kyra, Turn of X cube, Mona's X over X cube. And it becomes who the X goes to zero. So one third, one third times, one third plus some higher in terms of us, Hugh, over X cube. And finally it becomes to one third. And this is our limits for this for this question, all right.