Recent content by Dr Zoidburg

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    Question about graphing L(x,y) against f(x,y)

    The question I'm stuck on is this: Let f(x,y) = (x+1)^2 + y^2 I'm asked to find the partial derivatives and then evaluate them at (1,2). From there, find L(x,y), the linear approximation to f(x,y) at (1,2). That part I'm ok with. I got the following: f_x(x,y) = 2(x+1) f_y(x,y) = 2y...
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    Testing for convergence/divergence

    Thanks for the replies. It's helped me get my head around these problems better. I like jbunniii's solution. very clever and succinct. For this question: \lim_{n \to \infty} \frac {n^p}{a^n} = 0 my solution is: Apply L'Hopital's Rule: \frac{p}{ln(a)} [\lim_{n \to \infty} \frac...
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    Testing for convergence/divergence

    I've got a couple of problems I'm stuck on. Any help gratefully received! Test for convergence/divergence: \sum_{n=1}^{\infty} \frac {(n+1)}{n^3 ln(n+2)} What test should I do here? Can I rearrange the equation to be: \frac{(\frac{1}{n^2} + \frac{1}{n^3})}{ln(n+2)} and then use...
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    Linear programming bank assets problem

    I've got this question to do: A bank is attempting to determine where its assets should be invested during the current year. At present $500 million is available for investment in bonds, home loans, car loans, and personal loans. The annual rate of return on each type of investment is known...
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    Matrix forms of quadratic equations

    sorry I should have stated the problem a bit more in detail. Once I've got the eigenvalues, I'm to put them into the equation \lambda1x^2 + \lambda2y^2 = 9 so knowing which is which is important as swapping produces vastly different graphs with either: 9x^2 - y^2 = 9 giving x^2 - y^2/9 = 1...
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    Matrix forms of quadratic equations

    I have a problem with determining eigenvalues. This is what I've got thus far: Homework Statement Identify and sketch the graph of the quadratic equation 4x² + 10xy + 4y² = 9 The Attempt at a Solution We put it in the matrix form: \begin{pmatrix} 4 & 5 \\ 5 & 4 \\ \end{pmatrix} Now we find...
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    Word Problems In Algebra! Help Me Please!

    Question One: Train B travels 10km/hr faster than train A. Thus it's speed, relative to A, is 10km/hr. Train A leaves 1/2 hour earlier meaning, at 25km/hr, it's 12.5km ahead. So how long will it take train B, moving at a relative speed of 10km/hr, to travel 12.5km?
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    Solve this quadratic =(?

    think about it a second: you've already found that x^{2} - 8x + 11 Now you need to find y - 8y^{1/2} + 11 If you substituted x^{2} = y, you would have x^{2} - 8x + 11 which you already have the answer to. If x = 4+/-\sqrt{5}, what is x^{2} (i.e. y) going to equal?
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    Rate of change in distance question

    whoops. you're right there. scuttled. whoop! whoop! whoop! "Friends, help! A guinea pig tricked me!"
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    Rate of change in distance question

    yay, got it right! Off to the post office I scurry. And that other bit just came out poorly due to bad formating. It looks better in my assignment :wink:
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    Rate of change in distance question

    Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back. (In case you're wondering, I'm doing my studies by...
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    Find The Area of A Quadrilateral

    Sometimes it's easier to stick with whole numbers and fractions: length of side = \sqrt{3} length of QT = \frac{1}{2}\sqrt{3} area of triangle QTS = \frac{1}{2}*\frac{\sqrt{3}}{2}*\sqrt{3} =\frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2} and what does \sqrt{3}*\sqrt{3} = ? divide that by 4 (1/2 *...
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    Word Problem (Algebra?)

    Just a little. It wasn't helped by HoI using the wrong number! (it should read 10/3 not 4/3 - the 4/3 is correct but HoI skipped a line). Also you're only / by H in your equation whereas you should be / by W + H. Here's how I'd do it: Let's call the time taken to drive home x. Time taken...
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    Maximum area/volume problems

    Okay. Here's what I got for the box question: base of box = x, height = h. Volume of box = x²h = 2000; therefore h = 2000/x² Surface area of box = 2x² + 4xh Assume the sides cost $a p/cm². Then the total cost of the sides will be 4axh. Since the top and bottom cost twice as much (ie...
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    Maximum area/volume problems

    D'oh! I meant 12cm^{2} not 24. thanks for spotting that error. And thanks for the advice on Q2.