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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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u
4. Let f(x, y) = ey, where x = uv, y =
af
a) Use chain rule to compute and
af
du
Əv
b) Express your answer in a) in terms of u and v only and simplify.

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express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)= 1 2,−2.
express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)=− 2/3 ,2.
(a) express ∂w/∂u and ∂w/∂y as functions of uand y both by using the Chain Rule and by expressing w directly interms of u and y before differentiating. Then (b) evaluate ∂w/∂u and∂w/∂y at the given point (u, y). w = xy + yz + xz, x = u + y, y = u - y, z = uy; (u, y) = (1/2, 1)
(a) express ∂z/∂u and ∂z/∂y as functions of uand y both by using the Chain Rule and by expressing z directly interms of u and y before differentiating. Then (b) evaluate ∂z/∂u and∂z/∂y at the given point (u, y). z = 4ex ln y, x = ln (u cos y), y = u sin y;(u, y) = (2,π/4)
Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by W(f1,f2)=e2xW(f1,f2)=e2x. Are the functions that you found linearly independent on (−∞,∞)(−∞,∞)? How do you know?
Use the chain rule to find ∂z ∂s and ∂z ∂t . z = tan u v , u = 4s + 5t, v = 5s − 4t
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 3s + 9t, v = 9s − 3t ∂z/∂s=? ∂z/∂t=?
use an appropriate form of the chain rule to find dz/du and dz/dv. z=e^(5x^2y); x=(uv)^(1/2), y=1/v enter your answer in terms of u and v.
Use Chain Rule to find dz/du when u = 0, v = 1 if

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