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Determine the infinite limit.

$ \displaystyle \lim_{x \to \pi^-}\cot x $

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Adam R.

March 13, 2019

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

0:00

Determine the infinite lim…

01:32

Find the limit.$$\lim …

01:46

02:01

Find the limits.$$…

00:25

Determine each limit, if i…

00:53

02:57

01:45

01:12

Find the limits. Write $\i…

this problem Number thirty eight of Stuart Calculus. In addition, section two point two determined the intent limited the limit as experts his pie from the left of co tension of X. In order to do our estimation, we're going to assume that we I do not know how the function co attention behaves. And instead we want to relate it to functions that we may no more clearly or that are more familiar to us. So we're going to rewrite this limit is in the definition of the contention as a limit as X approaches pi from the left. Of course I know Vex divided by sign of X. And then now we want to use maybe a craft like the one to the right as a reference to determine the behaviour of each of these functions. As X approaches pine from the left to begin consented. Rex, as you approach pie from the left is this red plot this red function and as we approach price from the left approach a valley of approximately negative one or scientifics we see that sign increases hope until cry over too. Then decreases. And exactly at pine it is zero. However, approaching pie from the left gives it a value very close to zero from the left, Very close to zero. But, uh, various. A small positive number. As we can tell the numbers here, vehicle from a half to a quarter to maybe I've spent that's more like point one point zero zero one, right before reaching pie. This can be notated as such zero with the plus subscript to represent a very small positive number. And of course, when we take a fine name number only divided by a very small number you get an infinite amount. And due to the negative in the numerator, the entire limit is equal to negative infinity. To confirm the solution, we plot the function co attention around the value of pi and we see as we approach apartment from the left, the graph of the contention approaches negative infinity, and this confirms our solution for the limit

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