## MAT B41 — Week 4

Posted in 2018 -- MAT B41, Lecture Notes, Uncategorized by pgadey on 2018/05/29

Homework 2 is due! Homework 3 (tex) is now available.

Midterm information:

• Mock Term Test Friday 8 June @ 12:00-2:00 PM in IC-130
• Real Term Test Friday 15 June @ 3:00-5:00 PM in IC-130/230

All questions regarding format, question allocation, style of test, will be addressed by the Mock Term Test. I highly recommend you attend the Mock Term Test, because it will be the perfect preparation for the Real Term Test. More information will be available early next week.

In order to prepare for the Term Test, I recommend attempting the suggested exercises.

Suggested Exercises:

• 2.3 Differentiation: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 22, 24, 25 (Do as much as possible.)
• 2.5 Properties of Derivatives: 2, 3, 6, 14, 17
• 2.6 Gradients and Directional Derivatives: 1, 4, 6, 10, 11, 19

Past Term Tests:

2016 Term Test: Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ be given by $f(x,y) = (x+y)/x^2$.

1. Find an equation for the tangent plane to the graph $z = f(x,y)$ at the point $(2,3,f(2,3))$.
2. Find the direction of maximum increase in $f$ at the point $(2,3)$. What is the rate of maximum increase?

2015 Term Test:

1. Determine the rate of change in $f(x,y) = y - x^2 + z^2$ as you move from $(-1,0,2)$ towards $(2,4,2)$.
2. Compute the directional derivative of $f(x,y,z) = x^2y^3z^2$ at the point $(2,1,-1)$ in the direction of the upward normal for the plane $2x+y-2z = -7$.

Notes: