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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

    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

    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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    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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    Maximum area/volume problems

    [SOLVED] Maximum area/volume problems I have two here. One I feel I've solved but am just looking for reassurance (I'm needy that way!), The other I've got an answer but I know I've missed something. Homework Statement 1. A rectangle is inscribed in a 6/8/10 cm right-angle triangle where two...
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    Finding points of inflection

    Homework Statement Suppose the graph f''(x) of a function is given by: (see attachment) (a) Find all points of inflection of f(x) The Attempt at a Solution First I figured, by looking at the graph and seeing the intercept points [(-2,0),(0,0),(2,0)] that f''(x) = x^{4}-4x^{2} solving for...
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    Differentiation help

    Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here Homework Statement differentiate the following functions (you do not have to simplify): a. f(x)=(x-2)^{3}e^{-2x} b. f(x) = cos x / ln (x^{2} + x) c. g(t) = cos^{4}(t^{2} +...
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    Is this all correct? (more bl dy vectors!)

    Is this all correct? (more bl**dy vectors!) I hope these are right, but I have the nagging suspicion that they're not? Where have I gone wrong (if I have indeed gone wrong)? Homework Statement line P has equation (x+3)/2 = y = z-1 (a) Show that point Q (2,1,2) does not lie on line P. (b)...
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    Yet 'nother vector problem!

    Homework Statement following equations represent lines P nad Q in 3 dimensional space: P: 2-x=y+1=(z-3)/2 Q: 5-x=y-2=(z+1)/2 (a) Show that P & Q are two different lines which are parallel (b) Find the distance between the two lines, measured along a line perpendicular to P & Q. Homework...
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