Thomas Calculus 13th [Solutions]

plot(err(x), x 1..2, title #absolute error function#);
err( 1);
Chapter 3 Practice Exercises 199
Mathematica: (function, x1, x2, and a may vary):
Clear[f , x]
{x1, x2} { 1, 2};a 1;
_ 3 2
f[x ]: x x 2x
Plot [f[x], {x, x1, x2}]
lin[x _] f[a] f [a](x a)
Plot[{f[x], lin[x]},{x, x1, x2}]
err[x _] Abs [f[x] lin[x]]
Plot[err[x], {x, x1, x2}]
err//N
After reviewing the error function, plot the error function and epsilon for differing values of epsilon (eps) and
delta (del)
eps 0.5; del 0.4
Plot[{err[x], eps}, {x, a del, a del}]
CHAPTER 3
PRACTICE EXERCISES
1.
5 2
0.125 0.25
y x x x
dy
dx
4
5 0.25 0.25
x
x
2.
3 7
3 0.7 0.3
y x x
dy
dx
2 6
2.1 2.1
x
x
3.
3 2 2
3( )
y x x
dy
dx
2 2
3x 3(2x 0) 3x 6x 3 x( x 2)
4.
7
7 1
1
y x x
dy
dx
6
7 7
x
5.
2 2 dy
( 1) ( 2 )
dx
2
2( x 1)(2x 4x
1)
y x x x
2 2
( x 1) (2x 2) ( x 2 x)(2( x 1))
2
2( x 1)[( x 1) x( x 2)]
6.
y (2x 5)(4 x)
1
dy
dx
2 1
(2x 5)( 1)(4 x) ( 1) (4 x) (2)
2 2
(4 x) [(2x 5) 2(4 x)] 3(4 x)
7.
y
2 3
( sec 1)
dy
d
2 2
3( sec 1) (2 sec tan )
8.
y
1
csc
2 4
2 2
dy
d
2 1
2
csc csc cot
2 4 2 2
2
1 csc (csc cot )
2 4
9.
1 1
s 1 t t
t
1 t t
ds
2 t 2 t
1
2
2 2
1 t dt
1
t
2 t 1 t 2 t 1 t
10. s 1
t 1
ds
dt
( t 1) (0) 1
1
2 t 1
2 2
t 1 2 t t 1
11.
2 2
y 2 tan x sec x
dy
dx
2 2
(4 tan x)(sec x) (2sec x)(sec x tan x) 2sec x tan x
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