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Find the line through (3,1,-2) that intersects and is perpendicular to the line x= -1+t, y=-2+t, z=-1+t.

If (x',y',z') is the point of intersection, find its coordinates.

stuck with this one any help would be appreciated.

Passing throught point (1,-2,2) and is perpendicular to line v=(1,-2,2)+ t(1,-2,3).

I understand how it works for a single variable but im having problems with multivariable limits. Any tips in finding delta?

For example:

lim(x,y->0,0) (2x^2y)/(x^2+y^2)

Let f and g be functions such that 0≤f(x)≤g(x) for every x near c, except possibility at c. Use the definition of a limit to prove that if lim(x→c)g(x)=0 then lim (x→c)f(x)=0.

Please let me know what you think:

Definition: Limit lim(x→a)f(x)=L if and only if, given ϵ>0, there exists δ>0 such that 0<|x-a|<δ implies that |f(x)-L|<ϵ.

Given the definition of a limit we can state that lim(x→c)g(x)=0 has the following properties:

0<|x-c|<δ_0 Implies that |g(x)-0|<ϵ.

Also the lim(x→c)f(x)=0, 0<|x-c|<δ_1 implies that |f(x)-0|<ϵ.

By the given lim(x→c)g(x)=0 and 0≤f(x)≤g(x)

The value of f(x) is between 0≤g(x)

Therefore |g(x)-0|<ϵ_0= |g(x) |<ϵ. Thus δ_0= ϵ which is already given and this does not need to be proved.

Lets examine the target statement of lim(x→a)f(x)=0

Since 0<|x-c|<δ_1 It follows that |f(x)-0|≤|g(x) |<δ_1 where δ_1= ϵ.

Thus 0<|x-c|<δ therefore 0<|f(x)-0|≤|g(x)-0|< ϵ thus the lim (x→c)f(x)=0 holds.

If A and B are two non-empty subsets (of the same universe U), then A⋂B≠∅ or B⊆A'

Let A, B be two non-empty subsets.

if there exists an x such that {x belongs to A and x belongs to B} then A⋂B≠∅ done with first part of the proof.

Now lets assume that A intersect B is an empty set.

We can assume that there is a x in B because B its not an empty set. Also there is an element in A because its not an empty set.

Dont know where to take it from here.

Let A, B and C be sets. Show that if A-B⊆C, then A-C⊆B holds

I'm currently studying information theory and recently became interested in artificial neural networks (ANN).

I have some general questions regarding neurology and looking for answers or reading material. Any help would be greatly appreciated.

1. How do neurons wire themselves? The specific question is when a fertilized egg goes through its development process, and cells start becoming specialized in its functions, how do these new neurons connect? Are the synapses pre-wired? If so what process determines the wiring in the first place?

2. How many connections does a neuron have? Do if there is an upper limit, do some neurons have more connections then others? If so what stimulates new growth of synapses and how do they find other neurons to connect to? (I guess this is the same question as above.)

To be clear. I understand that the universe as we think of it today is not considered to be infinite. Yes it might be finite but unbound, but this is a hypothetical situation. I recently read a book called "The infinite Book" by John Barrows and he talks about the concept of infinity and how Cantor brought about the modern theory of sets (discrete mathematics).

One question that was posed in the book is the study of the universe before we knew the general shape before the discovery of the cosmic background radiation. He stated a figure of some order of magnitude that you would have to travel 100^100^100 million light-years (or something like that) IF the universe was infinite before you met a copy of yourself. I was wondering where the author got the figure from(no sources were stated.) How was the math calculated?

I'm trying to understand when said polynomial ƒ(x) = anx^n + an−1x^n−1 + ... + a2x^2 + a1x + a0 => 0. I found an answer that the leading coefficient must be positive and the degree of the polynomial is even. But why is this the case? Looking for a general case and trying to understand why. Some insight would be greatly appreciated.

When is a polynomial always >= 0?