# University of Waterloo Several Variables Mathematics Worksheet

Description

5 questionsThe coverage for this assignment is §2.1–2.5 and §4.1–4.2. §2.1–2.5 Vectors, Dot Products, Cross Products Lines and Planes §4.1–4.2 Functions of Several Variables. Limits and Continuity

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Problems
Q1. Let
х
=
and
W =
y
1
1
Find all vectors W, such that the vector ở x W is a multiple of
Q2. Find the equation of the plane determined by the points (1,0,0), (0,1,0) and (0,0,1).
Q3. Determine the magnitude of the orthogonal projection of the vector ✓ = [1,2,3] onto the
✓ 1
plane x + 2y + 2z = 7.

Q4. Create a contour map for the function f(x, y) = xy using c= -2,-1,0,1, 2.
=
=
Q5. Find two paths through the origin, such that, along these paths, the limit
4xy3
lim
(x,y)+(0,0) x2 + 2y6
presents different values.

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5 Questions

Tags:
limits

Continuity

Cross Products

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