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    Infinite series problem

    Ahh I see thanks for clarifying. I will reattempt the problem. EDIT: Got it by simply using integral test from n=3 to infinity. The integral converges so the series must as well. Thanks LCKurtz.
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    Infinite series problem

    The denominator is the first one you posted, n*(ln(n))^2 - n. In my book for the Limit Comparison Test it states "Let a[n] and b[n] be positive sequences." I assumed that "positive sequences" meant positive for all n [1, infinity). So it is really saying that if the sequence converges to a...
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    Infinite series problem

    Homework Statement Determine convergence or divergence using any method covered so far*: Ʃ(1/(n*ln(n)^2 - n)) from n = 1 to infinity *The methods are the following: - Dichotomy for positive series (if the partial sums are bounded above and the series is positive, the series converges) -...
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    Integration along y axis

    Verbatim: "In Exercises 27-44, sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis." ... 28). y = x^2 - 6, y = 6 - x^3, y-axis
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    Integration along y axis

    Homework Statement Compute the area as an integral along the y-axis: f(x) = x^2 - 6, g(x) = 6 - x^3 Homework Equations N/A The Attempt at a Solution I solve for x in terms of y for both equations and end up with: f(y) = +/-√(y+6), g(y) = (6-y)^(1/3) I then look for interception points...
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    Doubling time problem

    Ahhh, thank you so much.
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    First order linear differential equation

    Homework Statement dy/dt = k*y*ln(y/M), where M and k are constants. Show that y = Meaekt satisfies the above equation for any constant a. Homework Equations y' = ky y = P0ekt The Attempt at a Solution Taking the derivative of y, I get: (Meaekt)*(aekt)*k which is, ky*aekt ..and I'm...
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    Doubling time problem

    Homework Statement The only functions with a constant doubling time are the exponential functions P0ekt with k > 0. Show that the doubling time of linear function f(t) = a(t) + b at time t0 is t0 + b/a. Homework Equations n/a The Attempt at a Solution With initial time t0, P = at0 + b At...
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    Absolute value integral

    Homework Statement ∫0-->x |t|dt Homework Equations // The Attempt at a Solution 1/2*x^2 for x>= 0 1/2*(-x)^2 for x<= 0 Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).
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    Computer Science or Electrical/Computer Engineering?

    Unfortunately that is not available to me unless I double majored, but the CS degree and ECE degree have a good amount of overlap so getting a minor in CS would be easy.
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    Computer Science or Electrical/Computer Engineering?

    After doing some research, those huge layoffs to engineers in the past few years (even recently Boeing and HP layed off thousands of engineers) due to offshoring makes me lean towards CS, but I've also heard the same applies to CS, although job growth for software engineers is pretty high as the...
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    Computer Science or Electrical/Computer Engineering?

    Given that I am interested in both fields, which degree would give me the most job options after graduation (the degree is ECE, electrical and computer engineering)? For example, do employers consider applicants with an EE/CE (or in my case, ECE) degree when hiring software developers, or do...
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    Optimization problem using derivatives

    I would have never thought of doing it in that way.. Thanks for the insight and taking the time to help me..
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    Optimization problem using derivatives

    Here's what I got taking the derivative of the surface area, substituting h = 300/(pi*r^2) and l = sqrt(r^2 + (300/(pi*r^2))^2) SA(r) = pi*r*sqrt(r^2 + (300/(pi*r^2))^2) dSA/dr =...
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    Optimization problem using derivatives

    Is there also an easier way to do this than the way I'm doing it? I get such long, ugly derivatives and finding the zeros is really tedious and time consuming... This is an exam review problem so I don't think the problem should take this long. Is there another approach I could use? edit: I do...
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    Optimization problem using derivatives

    Man, I hate math... lol. Thanks.
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    Optimization problem using derivatives

    Homework Statement We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area. Homework Equations SA = pi*r^2 + pi*r*l where l is the slant height of the cone. V =...
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    Prove identity sec^-1(x) = cos^-1(1/x)

    Homework Statement Find and prove the identity sec^-1(x) in terms of cos^-1(arg) (Note that 1/cos^-1(x) is not equal to sec^-1(x). Homework Equations None. The Attempt at a Solution sec(sec^-1(x)) = x 1/cos(sec^-1(x)) = x 1/cos(cos^-1(x)) = 1/x 1/cos(cos^-1(1/x)) = 1/1/x...
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    Implicit differentiation

    Homework Statement Calculate the derivative with respect to x: x/y + y/x = 2y Homework Equations n/a The Attempt at a Solution I end up getting the right answer, but what I want to know is how to isolate dy/dx to one side after implicitly differentiating. I have tried differentiating the...
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    Find a relation between dx/dt and dy/dt

    Homework Statement A particle moves counterclockwise around the ellipse with equation 9x^2 + 16y^2 = 25. a). In which of the four quadrants in dx/dt > 0? Explain. b). Find a relation between dx/dt and dy/dt. c). At what rate is the x-coordinate changing when the particle passes the point...
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    Question about why ln(e^x) =/= x

    I could have sworn wolfram alpha was telling me the equation is false, but I just tried again and it told me the equation is indeed true :blushing:
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    Question about why ln(e^x) =/= x

    Why is ln(e^x) =/= x? The domain and range of the LHS are the same as the RHS, so I don't understand why this equation is false, where e^ln(x) = x, and the LHS and RHS of this does not have the same domain... I know that e^x and ln(x) are inverse functions, so please don't only tell me this...
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    Inverse derivative help

    My apologies, the question asks to find the g'(-1/2) where g(x) is the inverse of f(x) = x^3/(x^2+1). So the problem is actually really easy. Busted my *** for no reason trying to find the inverse function XD
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    Inverse derivative help

    Thanks for the reply but it's a first semester Calculus course. We haven't touched the topic of integration yet.
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    Inverse derivative help

    Homework Statement compute the inverse derivative of f(x) = x^3/(x^2+1) Homework Equations n/a The Attempt at a Solution My issue is a purely algebraic one... getting the inverse function! Attempting to solve for x yields no results! y = x^3/(x^2+1) y(x^2+1) = x^3 yx^2 + y = x^3 y = x^3 -...
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    Question involving higher derivatives

    Ohhh. I thought the question was asking for f to the kth power, not the kth derivative of f XD Thanks.
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    Question involving higher derivatives

    Homework Statement Which of the following satisfy (f^k)(x) = 0 for all k >= 6? a) f(x) = 7x^4 + 4 + x^-1 b) f(x) = sqrt(x) c) f(x) = x^(9/5) d) f(x) = x^3 - 2 e) f(x) = 1 - x^6 f) f(x) = 2x^2 + 3x^5 Homework Equations None, but given as a problem in a chapter where the topic is higher...
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    Average and instantaneous velocity

    Yes I'm sorry that's what I meant. But I don't understand, why can't you do what I did? If (v0 + v) / 2 = average velocity, and v0 and v are velocities at an instant in time, I don't understand how the second method doesn't work?
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