MATH100 Lecture Notes - Sinti, Classification Of Discontinuities

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harlequinbeetle750

15 Aug 2014

School

University of Alberta

Department

Mathematics

Course

MATH100

Professor

Ian Blokland

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MATH100 Full Course Notes

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Document Summary

Limits: limx->uf(x) = l means that f(x) -> l as x -> u from either side. Suppose x-> u with x < u only x u f (x) lim (x > u from the left) Or, x->u with x > u only x u+ f (x) lim (x->u from the right) ( x) = {+1, if x>0 -1, if x<0 f ( x)= 4 x2 (b) x 2+ f (x)=0 lim and x +2 f ( x)=0 lim. Now take reciprocals (this reverse the < to >) -> 1 > sin > cos ( ) A function is continuous if its graph can be drawn without lifting your pencil. Technical definition: f (x) is continuous at x = c lim x c. If f ( x)=f (c) (note: the 2-sided limit must exist & f (c) must be defined) Removable discontinuity when we can define f (c)

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!