MATH 2250 Lecture Notes - Lecture 1: Piecewise

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coralguinea-pig410

28 Mar 2018

School

University of Georgia

Department

Mathematics

Course

MATH 2250

Professor

Bergonio

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Document Summary

We start this section with an informal de nition of a limit. We write this as lim x a f (x) = l. These are respectively called the left limit and the right limit of f (x) as x approaches a. There are a few ways to evaluate a limit. Let f (x) = x2 3, g(x) = x 1, h(x) = x2 + 6x 7 x 1 j(x) = x2 3 x 1. The rst method is the tabular method, where you plug in values of x that are really close to the left and to the right of x = a. The drawback to this method is that these computations take a long time to do. Also, as you see from using g(x), the sequence doesn"t usually pop out. The second method is the graphing method, which would entail that you have a good knowledge of the graphs of functions, as well as possible shifts and re ections.

Related Questions

Hello,

Theproblem asks:
For what values of constants a andb is the function f(x) continous on (-infinity, + infinity) ?

x + 2 , x < 1
f(x) = a , x = 1
bx^2 , x > 1

If you have time, please read below and confirm or correct mythinking on this problem:

To me the problem is saying:

That as the limit of x approaches 1 from the left(1-) and/or from the right (1+); f(x) =3.

So, for the limit to be continuous, f(x) = 3 it will haveto be true [when x is/close to 1]for each of the three (piecewiseequations? what is the correct terminology?).

So I think that means a = 3 and b = 3 when x = 1 or xapproaches 1. To check this mathematically, do I solve for eachvariable? I.e. 3 = bx^2 and 3 = a?

Am I understanding this problem correctly? If you havetime, please explain (in writing) what this problem means and howto solve it.

Thanks!