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Question #10
Hi Randy,

I don't get limits for multivariable calculus and how the properties of limits apply. I am stuck on question #10 attached below and need some help on it.

Many Many Thanks,
Sam

I don't think there is anything tricky with this problem. Copying from your image I get

lim (x,y)->(-1,3) (x^2-xy)/(2x+y).

Just plugging in the limits for x and y I get { (-1)^2-(-1)(3) } / { 2(-1)+3 } = (1+3)/(-2+3) = 4.

Unless I'm missing something, this should be the answer.

If the denominator had come out 0, then there would be a problem. If the denominator and the numerator equaled 0 after substitution, then there is still hope, i.e., L'Hopital's Rule, which you may not have seen yet.

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#### randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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