Question

Given z=f(x,y),x=x(u,v),y=y(u,v), with x(1,3)=2 and y(1,3)=2, calculate zu(1,3) in terms of some of the values given in the table below.

Answer 1

The value of zu(1,3) using the data elements represented on the table of values is q + p

How to solve the calculus expression?

The given parameters are:

z = f(x, y)

x = x(u, v)

y = y(u, v)

Where

x(1, 3) = 2 and y(1, 3) = 2

To calculate zu(1,3), we make use of:

$z_u(1,3) = f_x(x,y) * x_u(1,3) + f_y(x,y) * y_u(1,3)$

The values x(1, 3) = 2 and y(1, 3) = 2 mean that:

(x,y) = (2,2).

So, we have:

$z_u(1,3) = f_x(2,2) * x_u(1,3) + f_y(2,2) * y_u(1,3)$

From the table of values, we have:

$f_x(2,2) = q$

$x_u(1,3) = 1$

$f_y(2,2) = 1$

$y_u(1,3) = p$

So, the equation becomes

$z_u(1,3) = q * 1 + 1 * p$

Evaluate the product

$z_u(1,3) = q + p$

Hence, the value of zu(1,3) is q + p

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