Recent content by zebo

Oh yeah, went alittle fast from my paper to here, sorry about that i ofcourse meant -1/(t*exp(t^2)) not 1/t+exp(t^2). I am heading to bed, but i will work on it tomorrow. It is not so much the solving of the integrals, but more the understanding behind why this shows that for all positive...

I don't know what you mean? I integrate it and get -1/a * exp(-at) = - 1/(a*exp(at)) which gives me the above answer when i use the upper and lower limit.

The first one, i assign t > a as the upper limit. When i solve it i get (-1/t)*(1/e^(t^2)) - (-1/a)*(1/e^(a^2)) = 1/(a*e^(a^2)) - 1/(t*e^(t^2)) . For t → ∞, the integral → 1/(a*e^(a^2))

Yes a is both in the lower limit and in the integrand in the assignment, was confused by this at first as well. I assign t > a in the first one, and t > 1 in the second one, and then i let t go towards infinity to show that they are convergent with the values i found when t goes towards...

Dont know what went wrong when i posted, but the integrals are meant to be read as from a to ∞ and 1 to ∞ for the functions exp(-at) and exp(-2at)

Homework Statement Prove that for every a ∈ ℝ+ the following improper integrals are convergent and measure its value. ∫a∞exp(-at)dt Edited by mentor: ##\int_a^{\infty} e^{-at} dt## ∫1∞exp(-2at)dt Edited by mentor: ##\int_1^{\infty} e^{-2at} dt## The Attempt at a Solution For the first...

Thank you all for your fast replies. Kahn academy is great, and i use it often for practice, but i just need a list of the different mathematical rules for different topics, since i have an exam coming up within the next couple of months. I can't memorize all the rules so a list would come in...

Hello, i just discovered this site and i love the work you guys are doing, helping people like me with math and physics etc. I was wondering if anyone knows a website / list / etc with math-rules, like algebra, logarithms, power, rules for differentiation, elasticity, substitution, sequence...

Thank you BvU and vela for your help :)

Im not sure my math professor would approve, i did something similar before and he did not like it.

Thanks! So as of now i have the following solution: f(x) = x^3, P(a,a^3), a=/=0, f'(x)=3x^2 TangentP = a^3+3a^2(x-a) In the point Q, TangentP = f(x) a^3+3a^2(x-a) = x^3 <=> x^2+ax-2a^2 = 0 x = a v x = -2a The tangent equals f(x) in P and Q, and P is located at (a,a^3). This means Q must...

I've tried again: 3a^2=(x^3-a^3)/(x-a) <=> 3a^2 = x^2+a^2+ax <=> x^2-ax-2a^2 = 0 d = b^2 -4ac <=> d=9a^2 x = (a+3a)/2a v (a-3a)/2a <=> x = 2 v x = -1 So one of the x is where P is and the other is where Q is ? or have i gone down a wrong path? I apologize if i am fumbling about with this...

Thank you for the fast response. Oh yeah i see, I am sorry about that i am snotty and heavy-headed. My biggest problem right now is i have no clue which direction i need to take to solve this. I want to find Q, without using any calculators, and the chapter which this problem is a part of does...

Homework Statement Disclaimer: English is not my first language, so i apologize for any wrong math-terms. We look at the function f(x) = x^3. On the graph for f we have a point, P(a,a^3), where a =/= 0. The tangent to f through P cuts through f in another point, Q. Find Q and show, that the...