Can someone tell me if Axler's texts use proofs? I'm looking for a book that teaches proofs at the high school level. Something other than a geometry text.
Question:
True or False If x^2<4 then |x|<=2
My solution:
I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
I've noticed that the first edition has 250 some odd pages and I believe the last edition has over 500 pages. Would I be missing out on any material if I bought an earlier edition? I have a limited amount of time so the shorter the text the better.
I also noticed it does not use Epsilon Delta...
Author: Edwin Moise
Title: Calculus Part 1 (1966)
Wondering if this would make a good text for self study.
https://www.amazon.com/dp/B00LUB1J2G/?tag=pfamazon01-20
I know about imaginary numbers but I don't think they apply here. Most texts I've looked at say the square root of a radicand squared is equal to the square of the radical. Yet, when you take the square root of negative number squared you get the positive root and when you square the square root...
An example would be the rational function x^2-4/x-2. In its original form it would have a hole at 2. Once its been factored and simplified there is no longer a hole.
Is a function with a removable discontinuity considered continuous? I've looked through about 6 calculus texts and none of them really go into any detail.
Can someone explain how these are equivalent.
sqrt((-3)^2) = (-3)^2/2
=sqrt(9) and (-3)^1
3 is not equal to -3
(-3)^2/2 can be expressed as:
(-3^2)^1/2 and (-3^1/2)2
(9)^1/2 and (sqrt(-1)sqrt(3))^2...
It's called a missing solution. You can read about them here: http://en.wikipedia.org/wiki/Extraneous_and_missing_solutions. Do you see that when you divide by x+5 there is the possibility that you are dividing by zero when x = -5? Since x^2-25 is a second degree equation you know there are two...