Recent content by Luscinia

Homework Statement Find the critical points for the function g(x, y, z) = x3+xy2+x2+y2+3z2. Homework EquationsThe Attempt at a Solution I've come up with the following 3 equations (derivatives set so that they are equal to 0) (1) 3x2+y2+2x=0 (2) 2xy+2y=0 (3) 6z=0 From (3), z=0 From (2)...

I think I managed to connect the dots together. I shouldn't have gotten rid of the -1 in |x2-1|. Instead, I should have just turned it into (x-1)(x+1) and move on from there. Assuming that x+1<1 and δ<1, -1<x-1<1 so if we add +2 to both sides, we get 1<x+1<3 |x+1||x-1|<3|x-1|<ε |x-1|<ε/3 But...

I will repetitively slam my head on a nearby hard surface until I get a bloody epiphany.

Homework Statement Calculate the value of the limit and justify your answer with the ε-δ definition of the limit. lim (x->1) x2 Homework Equations My professor gave us the hint that we have to take δ as 0<δ≤ k0 so that δ(ε)=min{k0,ε/ (k0+2)} I'm guessing that k0 is meant to be any number...

Even if the data was given to me, wouldn't I still be able to somehow get the same number by doing calculations though? I don't really care about the right or wrong answer at this point, I just want to know if there is more than 1 way of solving this problem.

Oh wow, that was much simpler than I thought. Thanks! I guess I jump to equations too quickly and automatically assumed that it was independent events by default.

Homework Statement Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient...

Homework Statement The internal energy of a perfect gas does not change when the gas undergoes isothermal expansion. What is the change in enthalpy? Homework Equations H=U+PV The Attempt at a Solution The answer is 0 Since U, the internal energy, doesn't change, I assumed that...

Help me connect the dots here, please! It's written in my notes that Reversible Compression have less work involved in comparison to irreversible compression while Reversible Dilatation have more work involved than irreversible dilatation. Why? My notes have the graphs and mathematical...

What's the difference between Cis/Trans and Z/E? Do they mean different things? And are they attributed differently. From what I understood, Cis/Trans are about Alkenes? Otherwise, when would it be appropriate to use Cis/Trans and when would it be appropriate to use Z/E? Also, what would...

Homework Statement Find the eigen values of the following mapping and determine if there are invariant lines. (2 -4) (-3 3) is the mapping. Homework Equations det (L-λI)=0 The Attempt at a Solution L-λI= (2-λ -4) (-3 3-λ) det(L-λI)=0=ac-bd=(3-λ)(2-λ)-12 ...

Oh man, can't believe I didn't see that. Thanks!

Homework Statement Find the equation of the plane passing through point A(2,1,0), B(3,-1,5) and C(2,2,1) Homework Equations Um..I don't know? The Attempt at a Solution Vector AB=(3 -1 5)^T-(2 1 0)^T=(1 -2 5)^T Vector AC=(2 2 1)^T-(2 1 0)^T=(0 1 1)^T perpendicular...

Homework Statement (All matrices are 2x2. Sorry for the awkward formatting) Find Matrix A such that (1 -1)-1 (2 3) (0 1 ) = (1 2) AT Homework Equations A1A2...Ak=Ak-1...A2-1A1-1 The Attempt at a Solution (1 -1)-1 (2 3) (0 1 ) = (1...

oops! I got it. It's a telescopic sum. I need to open my eyes a little more.