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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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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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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.

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