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    How do I sum this series?

    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?
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    Equilibrium point confusion

    No, it is (ab)^t, I forgot to specify the a and b going together. Thanks HallsofIvy! Very helpful :)
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    Equilibrium point confusion

    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...
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    MVT/Rolle's Theorem

    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...
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    Optimization problem

    Ah okay, thank you Mark44!!
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    Optimization problem

    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...
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    Optimization problem

    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...
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    Find the altitude of the satellite

    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 =...
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    Rate of change question

    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...
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    Having trouble solving this limit

    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 :(...
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    - need derivative help

    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...
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    Need help trying to do basic limit

    Supposedly I can simplify it to 1 ---- 2\sqrt{a}?
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    Need help trying to do basic limit

    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...
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    Help with proving a function can be written f = E + O

    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...
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    Help with proving a function can be written f = E + O

    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...
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    Help with proving a function can be written f = E + O

    i'm taking a calc theory class but I'm in 8th grade and my teachers made me skip a couple levels of math. I'm trying to get out of this class because I'm really struggling but they won't let me
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    Help with proving a function can be written f = E + O

    ok so in f(-x), E and O both equal f(-x) -f(-x), and in f(x), E and O are f(x) + f(x)?
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    Help with proving a function can be written f = E + O

    so for f(-x) = E(x) - 0(x): E(x) = f(-x) + O(x) O(x) = E(x) - f(-x) and for f(x) = E(x) + O(x): E(x) = f(x) - O(x) O(x) = f(x) - E(x) is that right? "Once you know what they must be if they are to work, then you can check to see if they actually do work. " how do I prove that there isnt a...
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    Help with proving a function can be written f = E + O

    for the first, both E(x) and O(x) are E(x) + O(x). For the second, both E(x) and O(x) are E(x) - O(x). i'm still a bit confused though because i started with what I wanted to show?
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    Help with proving a function can be written f = E + O

    I'm still a little confused. So here's what I did: for finding out what E is: f(x) = E(x) + O(x) f(x) - O(x) = E(x) (f-O)(x) = E(x) then for O: f(x) = E(x) + O(x) f(x) - E(x) = O(x) (f-E)(x) = O(x) Is that right? so then f(x) = (f-O)(x) + (f-E)(x)? i'm a little confused on what i'm supposed...
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    Help with proving a function can be written f = E + O

    Homework Statement a. Prove that any function f with domain R can be written f = E + O, where E is even and O is odd. b. Prove that this way of writing f is unique. Homework Equations The Attempt at a Solution Well, I didn't know where to start and I don't know where I'm...
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    Need help with a function problem?

    Homework Statement For which numbers a, b, c, and d will the function f(x) = (ax + b) / (cx + d) satisfy f(f(x)) = x for all x (for which this equation makes sense)? Homework Equations The Attempt at a Solution I'm not sure what to do, which is my problem. So far I think...
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    Towers of hanoi induction- slight bit i don't understand

    OHHH sorry that took me awhile! Thank you so much lol xD I have another question on a diff topic? I feel really stupid for asking but I'm not sure what to do. for proving this carefully: |x-3| = 8 I know you have to split it into two cases, x-3> 0. x-3 < 0. For x-3>0, x-3 = 8 x= 11. For...
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    Towers of hanoi induction- slight bit i don't understand

    Oh okay, i missed that, thanks. I'm still confused though...so the third line would be f(n+1) = 2(2n - 1) + 1, right? why is the next line 2(2n - 2) + 1?
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    Towers of hanoi induction- slight bit i don't understand

    Towers of hanoi induction-- slight bit i don't understand Homework Statement I am trying to prove towers of hanoi. Now I am on the induction part and there is a part I don't get. I have the whole thing, but i don't understand a couple lines. Homework Equations The Attempt at a Solution...
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    Where can I find practice induction questions online?

    I am quite slow at induction and I really need the practice. Where can I find induction questions online? Are there any sites also with answers just in case I get stuck?
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    Help with proving irrationality

    Does this mean anything at all for b? Proof by contradiction. Assume sqrt(n) is rational and n=/=m2 for any rational m. sqrt(n) = p/q where p,q are rational numbers. if n =/= m2, p/q =/= m. A rational number over a rational number has to rational. =><=
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    Help with proving irrationality

    From Spivak's 4th edition I'm having some difficulties knowing how to prove these things I need to prove. If someone could help me out, I would appreciate it. Homework Equations The book defines a prime number as this: A natural number p is called a prime number if it is impossible to...
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    X^n - y^n proof

    I definitely agree with you. I too am using Spivak's calculus book (my class just finished chapter 2, I'm a sophomore so I'm going a little slower through the book). But yeah start by multiplying the beginning terms you have, and the end terms you have. good luck!
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