Recent content by Calcgeek123

Yeah, the missing r is a type. Dividing makes sense though, duh. thanks so much!

Homework Statement Establish an equation in polar coordinates for the curve x^2+y^2=4y-2x Homework Equations n/a The Attempt at a Solution I know that x^2+y^2=r^2 so I used substitution, and now have r^2=4y-2x. Now this next part, I'm really not sure if I'm allowed to do this... i...

Thank you! I took the advice from the first post, and I've ended up with y-csc(t)=cos(t) (x-csc(t)). Now I'm just lost as to what to do with the point I've been given, (1/sq. rt of 3, 2/sq. rt of 3). I could plug in those numbers into the equation i arrived at for x and y, but then what would i...

Homework Statement Find the equation of the tangent line to f(t)=<cot(t),csc(t)> at the point (1/sq.rt of 3, 2/sq.rt of 3) Homework Equations n/a The Attempt at a Solution I started by finding the slope, y'/x', so I got csc(t)cot(t)/csc^2(t). I then used the equation of a line...

Homework Statement Given: the integral from 0 to infinity of t^(x)e^(-t)dt Problem: Determine f'(x). Homework Equations The Attempt at a Solution My teacher mentioned using the definition of a derivative: f'(a)= limit as x approaches a of f(x)-f(a)/(x-a). So far I have...

I found f(3)=6, f(4)=24, and f(5)=120. So f(x)=x! I need to also determine f'(x). I found f'(x)=t^(3)e^(-t). The next part of the problem says, what does this say about l'hospital's rule and factorials? I know that if i used l'hospitals rule, Id say that f(x)/g(x) = t^3/e^-t. I'm not sure...

That makes sense. Thank you! I integrated using the tabular method, and got that f(3)=-t^(3)e^(-t)-3t^(2)e^(-t)-6te^(-t)-6e^(-t) from 0 to infinity. Because one of the bounds includes infinity, I need to take the limit of this function as t goes to infinity. So i did that, and ended up...

I'm having trouble integrating it because of the t and x. t is a variable, and x is like a number. So when i let u=t^(x), du=xt^(x-1) ..is that correct? Its the x that is throwing me off...

Homework Statement Define the function: f(x)= The integral from 0 to infinity of t^(x)e^(-t)dt. Find f(3), f(4) and f(5). Notice anything? Homework Equations N/A The Attempt at a Solution I assume that I start by finding the integral of f(x). I used wolfram alpha and found that...

Or is this last part i did wrong?

That means.. that f^-1 will eventually be 3. To the left of that point though, it will have to be less than 4, and to the right of that point, it will hve to be greater than 2. ANd... this is why f^-1 can't be equal to the areas of the rectangle that its in..?

I made a sort of rectangle when I graphed. I have the points (1,2), (1,4), (7,4) and (7,2). From this, i see that the area below 2 is 12, and the area below 4 is 24..

Homework Statement Suppose f(2)=7, f(4)=1, and f'(x)< 0 for all x. Assuming f^(-1) is differentiable everywhere, establish that 12 < Integral from 1 to 7, of f^(-1)(x)dx < 24 Homework Equations N/A The Attempt at a Solution I do not know where to begin... =/

Oh, like e^(x) is the derivative of e^(x)?

How do i know that a function is equal to its derivative? (referring to f'(x) = f(x), and same with g(x)) Sorry..