Accelerated Multivariable Calculus Fall 2019
Review Problems
These review problems are meant as practice problems for the exam; they
will not be collected and graded. Disclaimer: these are just some of the types
of problems which might appear on the exam. Just because there is not a
problem here on a given topic does not necessarily mean that it will not
appear on the exam. Conversely, just because there is a problem here does
not mean that there will be a similar problem on the exam.
Stewart: Chapter 12 Review Problems pp. 842โ843: 1, 4, 5, 6, 11, 18, 19,
20, 26; Chapter 13 Review Problems pp. 882โ883: 6, 8, 17, 19; Chapter 14
Review Problems pp. 982โ984: 6, 9, 10, 13, 14, 19, 20, 25, 28, 43, 45, 47.
Note: there are answers to the odd numbered problems in the back of the
book.
Other suggested problems:
1. Let v= (โ1,1,3) and let w= (โ1,0,1).
(i) Find a unit vector uwhich points in the same direction as w.
(ii) Find the component of valong uand the (vector) projection pu(v).
(iii) Find vโpu(v) and verify that it is perpendicular to u.
(iv) Using (iii), compute the distance from vto the line through the origin
in R3and w.
(v) Compute the distance from vto the line through the origin in R3and
wby using the fact that the distance is equal to kvรwk/kwkand
check that it agrees with your answer in (iv).
2. Find the distance from the point pto the line Lgiven as the set of
all vectors of the form p0+tw, where p= (1,2,โ2), p0= (0,0,1), and
w= (1,1,โ3).
3. Find the distance from the point p= (2,โ1,3) to the plane defined by
the equation 2x+ 4yโz= 3.
