Assume that f is a continuous, real-valued function defined on a metric space X. If {xn} is a sequence in X converging to x, prove that Limn→∞f(xn) = f(x).
Here is my attempt, but I am not sure if it is correct.
My professor never really went over this concept clearly in Advanced Calculus.
The definition of an equivalent metric from my lecture slides:
Two metrics: d1 and d2 on a metric space X are called equivalent when there exists M >= 1 such that M-1d1(x,y) <= d2(x,y) <= Md2(x,y)
I am trying to...
Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance...
I know both are different courses, but what I mean is, will a proof based Linear Algebra course be similar to an Abstract Algebra course in terms of difficulty and proofs, or are the proofs similar? Someone told me that there isn't that much difference between the proofs in Linear or Abstract...
So far, I have taken General Chemistry I and II, and Organic Chemistry I. Out of these classes, only General Chemistry I seems to make use of the periodic table, but it is mostly just going through the basics of the periodc table. Not so much in Gen Chem II or Orgo I. I mean they give it to you...
Just a quick question, I was solving sin(x)=0 and cos(x)=0. I was trying hard to find out the solutions and the solutions were: for sin(x)=0------>x=0, pi, 2pi for cos(x)=0-------->x=pi/2, 3pi/2
But my question is why are those the solutions?
Homework Statement
Solve Laplace Transform L{tsin(2t)sin(5t)}
Homework Equations
cos(bt)=s/s^2+b^2
trig identity (product identity): sin(a)sin(b)=1/2[cos(a-b)-cos(a+b)
t^nf(t)=(-1)^nd^n/ds^nF(S)
(the template is complicated for me to use. Srry for the inconvinience)
The Attempt at a Solution...
Homework Statement
Homework Equations
The Attempt at a Solution
I am not asking to find the answer, just wanted to know whether to use the variation of parameters or undetermined coefficients. Because this was on a test problem and I used variation of parameters instead. I know it is a...
Homework Statement
y''-16y=2e^4x. Find general solution
Homework Equations
The Attempt at a Solution
I have the homogenous equation which is c1e^-4x+c2e^4x, but I'm trying to find the particular solution for 2e^4x. I did yp=ae^4x, yp'=4ae^4x, yp''=16ae^4x, then plugged it into the equation...
Homework Statement
Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases
r(t)=<t, 2-t, 2t>
Homework Equations
parametric equation (can't type the equation, too confusing to use the template)
The Attempt at a Solution
So far, I have <1...
Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases
r(t)=<t, 2-t, 2t>
So far, I have <1, -1, 2> and points (0, 2, 0). Am I even correct? And how do I sketch the graph. I know it's suppose to be in the xyz graph, but how do I graph the...
Hi. I have a question about Organic and Physical Chemistry. I have already finished General Chemistry I and II and got decent scores on both of them (B on both of them). I am interested in taking Organic Chemistry, then Physical Chemistry afterwards. I know that both are different from General...