## MAT B41 — Week 5

**Mock Midterm this Friday 12-2pm in IC 130. Midterm Test next week!**

Several people asked about Question 7 off of Homework #3. The intent of the question was for to be undefined. This is different from the textbook, where the function is given explicitly. You may write and without knowing the function .

**Additional resources:**

- Wikipedia on Clairaut’s theorem
- Khan Academy on Second Partial Derivatives
- Krista King on Second Partial Derivatives
- PatrickJMT on Second Partial Derivatives
- ThreeBlueOneBrown on Single Variable Taylor Series
- Mark Ancliff on Multivariate Taylor Series

**Suggested Exercises:**

- 3.1 Iterated Partial Derivatives: 1, 2, 3, 4, 5, 6, 7, 12, 14, 15, 16
- 3.2 Taylor’s Theorem: 1, 2, 5, 9

**Past Term Tests:**

*2016 Term Test*:

Give the 4th degree Taylor polynomial about the origin of .

*2015 Term Test*:

- Compute the 4th degree Taylor polynomial about the origin of .
- Find the linear approximation to the function at the point and use it to estimate .

**Notes:**

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