Week15Discussion

Chapter 12.5

Problem 7

Solve for t = 1 when:

\(z = 3x + 4y\)

\(x = t^2\)

\(y = 2t\)

\(f_x(x,y) = 3\)

\(f_y(x, y) = 4\)

\(\frac{dx}{dt} = 2t\)

\(\frac{dy}{dt} = 2\)

\(\frac{dz}{dt} = 3(2t) + 4(2) = 6t + 8\)

Solve for t = 1:

\(t(1) = 14\)

Problem 11

Solve for t = \(\frac{\pi}{4}\) when:

\(z = x^2 + 2y^2\)

\(x = sint\)

\(y = 3sint\)

\(f_x(x,y) = 2x\)

\(f_y(x, y) = 4y\)

\(\frac{dx}{dt} = cost\)

\(\frac{dy}{dt} = 3cost\)

\(\frac{dz}{dt} = 2x(cost) + 4y(3cost)\)

Substitute in x and y:

\(\frac{dz}{dt} = 2(sint)(cost) + 4(3sint)(3cost)\)

Solve for t = 1:

\(t(\frac{\pi}{4}) = 19\)

Valuable Elements

• I enjoyed the refresher on matrices and how they solved many data science problems. An example would be how SVD can find which words are grouped together in many texts. This can be beneficial in neural networks and machine learning.