AMS 11A Chapter Notes - Chapter 10.1: Constant Function

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sangriaferret24

2 Oct 2016

School

UCSC

Department

Applied Math and Statistics

Course

AMS 11A

Professor

katznelson

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Document Summary

Limit: the notion of getting closer and closer to something, but yet not touching it. Example: in the equation , as the value of x increases and gets closer to 1, the value of y gets closer to 3. The limit of f(x) as x approaches 1 is 3, or. The limit of f(x) = x + 3 as x approaches 2, or , is 5. The limit of f(x) as x approaches a is the number l, written: When finding a limit, we are not concerned with what happens to f(x) when x equals a, only what happens when x gets close to a. Also, the limit has to be the same whether x approaches from the left or the right. Estimate *** to get closer because the limit of f(x) as x approaches 2 appears to multiple numbers, we have to conclude that it doesn"t exist.

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!