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# For the limit $$\lim_{x \to \infty} \sqrt{x \ln x} = \infty$$ illustrate Definition 9 by finding a value of $N$ that corresponds to $M = 100$.

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Limits

Derivatives

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

this problem Number seventy four of this tour Calculus C edition section two point six for the limit. The limit his expertise, Impunity of the square root of the quantity X Alan X equals infinity. Illustrate definition nine by finding a value and that corresponds to M equals one hundred Intuit call. We're looking for her Valium X. Such Stan as X is greater than in. We can guarantee that the function f we'LL always be greater than the value em in this case and is one hundred. So we're looking for a place on the graph that corresponds to the function being greater than one hundred. So I take it plotting, planning tool Take the square root of that, uh, function Excel next and thought that function in red here. And then we notice that the function definitely a purchasing committee, is expert is infinitely. But in order for us to confirm this proof we needed to find about it affects such that we can guarantee that the function is greater than one hundred specifically for him. For this, my ex and with some child there were able to identify the value of X the end to be thirteen eighty three. So X must be greater than thirteen. Eighty three and it's thirteen eight. Three is inappropriate. Mallie for this problem on this corresponds Sam is one hundred.

#### Topics

Limits

Derivatives

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp