Page 105 - A Guide to MATLAB for Beginners and Experienced Users

Practice Set B

Calculus, Graphics,

and Linear Algebra

Problems 2, 3, 5–7, and parts of 10–12 require the Symbolic Math Tool-
box. The others do not.

1. Use contour to do the following:
3
3
(a) Plot the level curves of the function f (x, y) = 3y + y − x in the
region where x and y are between −1 and 1 (to get an idea of what
the curves look like near the origin), and in some larger regions (to
get the big picture).
3
3
(b) Plot the curve 3y + y − x = 5.
(c) Plot the level curve of the function f (x, y) = y ln x + x ln y that con-
tains the point (1, 1).
2. Find the derivatives of the following functions. If possible, simplify each
answer.
3
2
(a) f (x) = 6x − 5x + 2x − 3.
2x−1
(b) f (x) = .
2
x +1
2
(c) f (x) = sin(3x + 2).
(d) f (x) = arcsin(2x + 3).
√
4
(e) f (x) = 1 + x .
r
(f) f (x) = x .
2
(g) f (x) = arctan(x + 1).
3. See if MATLAB can do the following integrals symbolically. For the indef-
inite integrals, check the results by differentiating.

π/2
(a) cos xdx.
2
(b) 0
x sin(x ) dx.
√

(c) sin(3x) 1 − cos(3x) dx.
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