Homework Statement
1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ...
Homework Equations
The Attempt at a Solution
The only headway I've made is that this is ∑ n/(2^n). how do I go about summing this?
Homework Statement
I was sick today, and here is what my friend told me. I don't quite understand the question, but apparently we talked about equilibrium points, and for homework, we have to take the derivative of P(t)= 1/((ab^t)+(1/c)), put it in terms of P, and get P'(t)=(P-6)(-k)P...
Homework Statement
Define interval where a) MVT applies, b) Rolle's applies, c) MVT doesn't apply. explain. (In this, we're saying Rolle's is f(a) = f(b), not f(a) = (f(b) = 0.
Homework Equations
The Attempt at a Solutionf(x) = (x-4)^(2/3)
a) for MVT, must be cont on [a,b] and...
Ah okay, thanks I'll fix that up.
Actually I don't currently have a graphing calculator, but i just plotted it out on an online one. To make sure the graphing calculator wasn't faulty, is x = .799999? Sometimes the online ones are a bit sketchy.
Thanks for your help!!
Anyone know about the...
Homework Statement
Find the abs max and abs min values of the function
f(x) = -2x^2 + 3x + 6x^(2/3) + 2.
Homework Equations
The Attempt at a Solution
So the candidates are the endpoints, where f'(x) = 0, and where f(x) DNE.
f(-1) = 3
f(3) = 5.481
For the derivative of...
Homework Statement
At the instant when theta is 120 degrees, the angle theta is increasing at the rate of 2.7 degrees per min. Find the altitude of the satellite and the rate at which the altitude is changing at this instant. Express the rate in units of mi/min.
Homework Equations
r =...
Homework Statement
Find any and all points inside the interval (0,3) where the instantaneous rate of change of f equals the average rate of change of f over the interval [0,3], for the equation
f(x) = 4x^2 - x^3
Homework Equations
The Attempt at a Solution
Not really sure how...
Homework Statement
lim (1+(a/x))^(bx) as x-->infinity
Homework Equations
The Attempt at a Solution
so, i raised the limit to e, and said e^lim(as x->inf) bxlog((a/x)+1). Then I pulled the constant b out and put it outside of the lim... I don't know how to do the rest though :(...
urgent -- need derivative help!!
Homework Statement
f(x) = sin^3(x^2 + sinx)
f(x) = (cosx)^31^2
f(x) = sin(x^3/(cosx^3))
Homework Equations
The Attempt at a Solution
f(x) = sin^3(x^2 + sinx)
so i said it was 3sin(x^3+sinx) * (2x+cosx)
f(x) = (cosx)^31^2
i said...
Homework Statement
lim
_{}h\rightarrow0 (\sqrt{a+h} - \sqrt{a}) / h
3. ok so i multiplied by \sqrt{a+h} + \sqrt{a}. The top simplified to a+ h -a, aka h. the bottom is h(\sqrt{a+h} + \sqrt{a}).
The h cancels, so I am left with
1 / (\sqrt{a+h} + \sqrt{a}
how do i simplify this...
Okay i just googled how to solve for two equations simultaneously, I don't know if i didi this right. But I went:
f(-x) = E(x) - O(x)
O(x) = E(x) - f(-x)
so then
f(x) = E(x) + E(x) - f(-x)
-2E(x) = -f(-x) + f(x)
then can I divide by -2? I'm so sorry I have a feeling i'm being really slow...
I don't know what i've had. back in 5th grade I was ahead of my class so my teacher had me do other stuff, and that's kind of what I've been doing for the past couple years. I've never taken an official course like geometry or algebra II, I've just kind of done what they've told me to do :( and...