Recent content by lelandsthename

Homework Statement How does the speed of light's finiteness limit the size of our observable universe? Using the speed of light (c = 3 x 10^8 m/s), estimate the age of the observable Universe in years given its estimated size of about 10^26 m. Homework Equations The Attempt at a...

Well the crazy results come when i plug my answer into y=. The program keeps telling me that I am incorrect with \sqrt{7x^4}+((7x^{18})/6) (that's to the 18th)

What am I doing wrong?? - Linear Differential Equations Homework Statement Hi everyone, the problem I have is listed under my attempt (I hope it's ok that I pasted it): to solve the below linear differential equation with the initial condition y(1)=1 Homework Equations P(x) and Q(x) linear...

Hmm, ok, so dv = dy/dx? Somehow I still think I'm missing something. Shouldn't there be a dv/dx somewhere or something? I am just not seeing it =/

Homework Statement Solve xy' = y + xe^(y/x) using the substitution v=(y/x) Homework Equations Solving differential equations, substitution The Attempt at a Solution x (dy/dx) = y + xe^(y/x) (dy/dx) = (y/x) + e^(y/x) Substituting v=(y/x) (dy/dx) = v + e^(v) I do not know...

haha! ok I will give it a try with k first, it'll even make it look neater! :smile: and thank you for helping me with the limit! So because the limit equals one then the answer will just be -k?

Homework Statement Hey everyone! I have another question about improper integrals, they're so hard! M = -k \int\stackrel{inf.}{0} te^(kt) dt When k = -0.000121 (Carbon 14's constant, we are solving for the mean life of a carbon-14 isotope) Homework Equations Improper integrals...

Homework Statement Lim ((e^{2})-(\frac{t-3}{3}( * e^^{\frac{t}{3}}))) t -> -\infty [sorry for the formatting, I tried my best! that is "The limit as t approaches negative infinity of e squared minus (t-3/3) e to the t/3)]"] Homework Equations I am solving improper...

Well, I see how splitting it up makes more sense than tackling it, but I don't know what to substitute u for to get rid of both the (x - (1/2) and x. And for the arctangent, how do I go about that? I do know how to set up a trig substitution with a radical, when I must draw a triangle and find...

ok so I got the completing the square but how on Earth can I continue? I just don't see it... \int\frac{x-2}{(x-\frac{1}{2})^{2}+\frac{3}{4}} dx

Homework Statement \int\frac{-\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1} dx Homework Equations Completing the square, partial fractions The Attempt at a Solution I think I need to complete the square to do this but I can't figure out how to do it. Also, do I need to separate the...

Homework Statement If f is differentiable at x=0 and g(x) = [f(x)]^2, f(0) = f'(0) = -1, then g'(0) = Homework Equations MC Answers: (A) -2 (B) -1 (C) 1 (D) 4 (E) 2 The Attempt at a Solution The only thing I could think of was that if g(x) = (f(x))^2 then g'(0) = (f'(0))^2...