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Determine (a) $\lim _{x \rightarrow 5^{-}} f(x)$ (b) $\lim _{x \rightarrow 5^{+}} f(x)$ (c) $\lim _{x \rightarrow 7^{-}} f(x)$ (d) $\lim _{x \rightarrow>7^{+}} f(x)$(e) $\lim _{x \rightarrow 9^{-}} f(x)$ (f) $\lim _{x \rightarrow 9^{+}} f(x)$ (g) at which $x$ -values is $f$ discontinuous, and classify the discontinuities. (h) graph the function.

(a) 25(b) 25(c) 49(d) 49(e) 59(f) 60(g) $x=9$(h) the answer s graph

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:28

Given the graph of $f(x)$ …

01:07

Use the given graph to fin…

01:33

For the function $f$ whose…

So for this problem, we can go ahead and begin by finding part A, which is the limit as X goes to negative infinity of our graph FX. And we can see that as our graph continues to the left, it's going to approach zero, um, and then part B s for the limit as excursion positive infinity of ethics. And we can see that on the right side of this last little portion, I'm over here Over here is continuing to get closer to zero. Um, but it also is going to approach the ass. And tote of X is equal to any wise equal to zero. Um, Parsi access asks us of to find the limit as Ex Purchase three from the left side of ethnics. So as we start on the left side here and go this way, we can see that or a graph is going to be approaching. Um, this point right here, which is that wise equal to one, even though there's a whole, it's still approaching that point, and the same thing for as experts is three from the right hand side. Um, it's also going to be approaching that same value of one. I'm next f of three is actually undefined. And lastly, we want to find our discontinuities, Intergraph, So we can see that one point is going to be at X is equal to negative three right there where we have a break on the left side. And we also have a hole at X is equal to positive three. And lastly, we have an ass into right here at X is equal to five.

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