Thomas Calculus 13th [Solutions]

538 Chapter 7 Transcendental Functions
24.
1 1 1 1
y f ( x) y 1 y 1 x f ( x) 1 ;
x x y 1 x 1
1
f f ( x) 1 1 1 ( x 1) x;
f ( x)
1
x 1
1
1 df
1
2
x dx
f ( x)
f ( x)
1
df
dx
1 1
f ( x) ( x 1)
( ) 1 1
f 1 f ( x)
1 1 x and
1 1
2 2
1
f x
x
1 1
x x
2
x ;
dy
25. y ln x 1 ;
dx x
dy dy dx dy 1 1 dy
x
1 m/sec
dt dx dt dt x x dt 2
e
e
26.
x/3 dy x/3
y 9e 3 e ;
dx
1
4
3 3
e e
1 5ft/sec
1
4
( / )
9
dx dy dt dx
dt ( dy/ dx) dt 3e
x/3
y
;
x 9 y 9e
3
dx
dt x
9
1
9
9
4
e
3
3
e
3
27. K ln(5 x) ln(3 x) ln 5 ln x ln 3 ln x ln 5 ln 3 ln 5
3
28 . (a) No, there are two intersections: one at x = 2 and the
other at x = 4
(b)
Yes, because there is only one intersection
29.
ln x
log4
x ln 4 ln x ln 2 ln 2 ln 2 1
log2
x ln x
ln 2
ln 4 ln x ln 4 2ln 2 2
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