t9u ati 15. Find the partial derivatives— of u = X2 + yz where x =pr cos °, y pr sin 0, z p r. or, ar ao 16. Let C1-1,11 )lave the inner product 1 (p, q) = p(x)q(x)dx. —1 (a) Show that pi (x) 1 and...

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t9u ati 15. Find the partial derivatives— of u = X2 + yz where x =pr cos °, y pr sin 0, z p r. or, ar ao 16. Let C1-1,11 )lave the inner product
1 (p, q) = p(x)q(x)dx. —1 (a) Show that pi (x) 1 and p2(x) x are orthogonal. (b) Let p3(s) a + bx cx2, Calculate (pi, p:) and (p2, p3) in terms of a, b. c. (c) Find p3 so that {2)1,1)2, p3} is orthogonal,

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Answered Same Day Dec 27, 2021

Solution

Robert answered on Dec 27 2021

116 Votes

x , y and z are as given in the question
x = p * r * cos θ
y = p * r * sin θ
z = p + r
u = x^2 + y * z = (p^2) * (r^2) * ((cos ^2) θ) + (p^2) * r * (sin θ) + p *
(r^ 2) * ( sin θ)
du/dp = 2 * p * (r ^ 2 ) * ((cos ^2) θ) + 2 * p* r *(sin θ) + (r ^2) * p *
(sin θ)
du/dr = 2 * (p^2) * r * ((cos ^2) θ) + (p^2) *...

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t9u ati 15. Find the partial derivatives— of u = X2 + yz where x =pr cos °, y pr sin 0, z p r. or, ar ao 16. Let C1-1,11 )lave the inner product 1 (p, q) = p(x)q(x)dx. —1 (a) Show that pi (x) 1 and...

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