Graphics Programs Reference
In-Depth Information
6. Use
simplify
or
simple
to simplify the following expressions:
(a) 1
/
(1
+
1
/
(1
+
1
x
))
(b) cos
2
x
−
sin
2
x
7. Compute 3
301
, bothas an approximate floating point number and as an
exact integer (written in usual decimal notation).
8. Use either
solve
or
fzero
, as appropriate, to solve the following equa-
tions:
(a) 8
x
+
3
=
0 (exact solution)
(b) 8
x
+
3
=
0 (numerical solution to 15 places)
(c)
x
3
+
px
+
q
=
0 (Solve for
x
in terms of
p
and
q
)
=
8
x
−
4(
all
real solutions). It helps to draw a picture first.
9. Use
plot
and/or
ezplot
, as appropriate, to graphthe following functions:
(a)
y
=
x
3
(d)
e
x
−
x
for
−
4
≤
x
≤
4.
(b)
y
=
sin(1
/
x
2
) for
−
2
≤
x
≤
2. Try this one with both
plot
and
ezplot
.
Are bothresults “correct”? (If you use
plot
, be sure to plot enough
points.)
(c)
y
=
tan(
x
/
2) for
−
π
≤
x
≤
π,
−
10
≤
y
≤
10 (
Hint
: First draw the plot;
then use
axis
.)
(d)
y
=
e
−
x
2
and
y
=
x
4
−
x
2
for
−
2
≤
x
≤
2 (on the same set of axes).
10. Plot the functions
x
4
and 2
x
on the same graph and determine how many
timestheirgraphsintersect.(
Hint
:Youwillprobablyhavetomakeseveral
plots, using intervals of various sizes, to find all the intersection points.)
Nowfindtheapproximatevaluesofthepointsofintersectionusing
fzero
.
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