MTH164FA10-M1d_ans

First observe that using implicit dif z dx dy as

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Unformatted text preview: 16+25 A second approach follows the second method in part (b) above. ∂z ∂z dz = ∂ x dx + ∂ y dy where the partial derivatives were calculated ∂z ∂z ferentiation. Then start rewriting this as dz = ￿ ∂ x , ∂ y ￿ · ￿dx, dy ￿ ￿4, −5￿ · ￿dx, dy ￿ = ￿￿4, −5￿￿ ￿￿dx, dy ￿￿ cos(θ) and finally continue late the direction of maximum increase. First observe that using implicit dif= ∇z · ￿dx, dy ￿ = as before to calcu- These two approaches say exactly the same thing, but they use slight different notation. Both notations are widely used so it’s important to get used to translating between the two. (d) Find the directional derivative of z = f (x, y ) at P (2, 1, −1) in the direction ￿...
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This document was uploaded on 05/06/2013.

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