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# 1.3 Limits Graphical And Analytical Connectionsap Calculus

Section 1.3 The Limit of a Function and section 1.4 Calculating Limits The notion of a limit forms the foundation for all of calculus. In section 1.3 you will consider limits intuitively, from a numerical viewpoint, and from a graphical viewpoint. Numerical investigations help. This lesson contains the following Essential Knowledge (EK) concepts for the.AP Calculus course. EK 1.1B1 EK 1.1C1 EK 1.1C2 Click here for an overview of all the EK's in this course. AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site. 1.3 Finding Limits Analytically, involving Trig functions (Watch before Day #73 lesson) This video assumes that you've already learned in class or elsewhere that the limit as x→0 of sin(x)/x =1.

I want to talk about limits, limits are really important concept in Calculus, they're in everything in Calculus.
Let's start with the function f of x equals x cubed minus 125 over x-5, then you'll notice that this function is not defined of x=5 but we can still figure out what happens near x=5 and that's what limits are all about. So let's observe I've got I've made a table of values here and I have the inputs for 4, 4.9, 4.99, 4.999. These inputs are approaching five, what are the values doing? Well 61, 73.5 something 74.8 something, you can see that these outputs 9are getting closer and closer to it appears 75.
Now let's see what happens on the other side, so x is coming in towards 5 from the right now, 6, 5.1, 5.01 what's happening to the outputs. 91, 76.51, 75.15 75.015 you can see that here as well the values are getting closer to 75. So you can't plug 5 into this function but you can get as close as you want, and as you get closer and closer to 5 form both sides the value of the function is approaching 75. So here's what we say, we say that f of x approaches 75 as x approaches 5 or another way to write this and this is the way we will commonly express it the limit as x approaches 5 of f of x is 75.

I. Functions, Graphs, and Limits

Analysis of graphs. With the aid of technology, graphs of functions are often

easy to produce. The emphasis is on the interplay between the geometric and

analytic information and on the use of calculus both to predict and to explain the Java update for mac.

observed local and global behavior of a function.

Limits of functions (including one-sided limits)

• An intuitive understanding of the limiting process.

• Calculating limits using algebra.

• Estimating limits from graphs or tables of data.

### 1.3 Limits Graphical And Analytical Connectionsap Calculus Pdf

Asymptotic and unbounded behavior

• Understanding asymptotes in terms of graphical behavior.•

Describing asymptotic behavior in terms of limits involving infinity. • Comparing relative magnitudes of functions and their rates of change (for example, contrasting exponential growth, polynomial growth, and logarithmic growth).

Continuity as a property of functions

• An intuitive understanding of continuity. (The function values can be made as

close as desired by taking sufficiently close values of the domain.)

### 1.3 Limits Graphical And Analytical Connectionsap Calculus Answers

• Understanding continuity in terms of limits.

• Geometric understanding of graphs of continuous functions (Intermediate

### 1.3 Limits Graphical And Analytical Connectionsap Calculus Solution

Value Theorem and Extreme Value Theorem).