mike

What equations would I use to solve this? I tried the Lorentz Transform and I'm not getting the right answer!

There are two planets (A and B) 10000ly apart. In the galaxy's reference frame, 2 events occur (one on each planet) 45000 years apart (Event on planet A occurring at t = 0 years and event on planet B occurring at t = 45000 years). For an

Prove lim x^2 as x -> 1 = 1

After doing scratch work, is the format of this proof correct?

Proof: GIven ε > 0, Let δ = min(1 , ε / 5).

If |x - 1| < δ

3|x - 1| < 3δ

|x+1||x-1| < 3|x-1| < 3δ,

then |x^2 - 1| < 3(ε / 3)

|x^2 - 1| < ε

Q.E.D.

I have a page of examples of solving epsilon - delta proofs. Upon proving that lim x -> 2 (x^2 + x - 2) = 4, the page says " the right hand side is at the minimum when x + 3 is at its maximum. Since the maximum of x + 3 is 6, we know that,

|x - 2| < e / |x + 3| < e / 6

My question is if the maximum of x + 3 is 6, wouldnt all values of x make that inequality false (e / 2 < e / 6 is false for example)?

This is the page (example 4) for reference.

https://www.ocf.berkeley.edu/~yosenl/math/epsilon-...

How do I prove this limit?

lim x -> 2 (1/x) = 1/2

0 < |x + 3| < 6

|x+1| > x+2

Using algebra i break up the inequality to the following:

When x >= -1 , x+1 > x+2

When x < -1 , -x-1 > x+2

However, when i solve this, I can't get the right answer. How do i do it?

|2x + 4| < x

Thanks in advance :)

How do you do this limit? Thanks in advance!

lim x -> infinity of sqrt(x^2 + x) - x

Please Help. Thanks in advance!

40ml of 0.35M CH3NH2 is titrated with 0.28M HCl until the end point. Calculate the pH at endpoint. Kb = 5 * 10^-4.

Hi! How do you do this problem?

A train traveling at a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to

an angle of 17.5º throughout the curve. What is the speed of the train?

How do you do this limit?

lim x->0 [cos(2x) - 1] / [2x^2]

If the triple scalar product of the normals is 0, and none of the normals are scalar multiples of each other, does that mean that the 3 planes will always intersect in a line?

Find the sum from n=2 to infinity of (e^(1/n))/(n^2).

I'm getting that it converges because the antiderivative is -e^(1/x) and that approaches 1 as x approaches infinity, meaning that both the improper integral and series converges; but the textbook says it diverges.

Find the sum from n=1 to infinity of (1+2^n)/(3^n).

How do you do this problem?

(x-2)/6 = (y-4)/3 = (z+8)/2

Given a quadratic of the form f(x) = x^2 + bx + c, prove that the equation f(x) - f(a) = 0 will always have 2 integer solutions for all a,b,c ϵ ℝ, or provide a counter example to disprove the statement.

I noticed, while doing epsilon delta proofs, that if I have a quadratic, like f(x) = x^2 - 3, then all polynomials of the form x^2 - 3 - f(a) can be factored if a is a non-negative integer. Why is this?

How come if 4 < x+3 < 6, then |x+3| < 6?

Find the area of the largest rectangle enscribed by y = x^2 and y = 5

Prove x^2 / (x+1) = x - 1 + 1/(x+1) for all x =/= -1.