Page 207 - Calculus Demystified

CHAPTER 6
Transcendental Functions
194
√
We leave it to you to perform the calculation and discover that 24 ft is the
optimal distance at which the viewer should stand.
You Try It: Redo the last example if the tapestry is 20 feet high and the bottom
of the tapestry is 6 inches above eye level.

Exercises

1. Simplify these logarithmic expressions.

2
a · b −3
(a) ln
4
c · d
2
log (a b)
3
(b)
2
log (a b)
2
4
(c) ln[e 3x · z · w −3 ]
√
w
(d) log [100 · 10]
10
2. Solve each of these equations for x.
x
x
(a) 3 · 5 −x = 2 · e 3
3 x
x
(b) = 10 · 10 2
5 −x · 4 2x
(c) 2 3x · 3 4x · 4 5x = 6
5 2
(d) =
x
2 3x · e 5x 2 · 3 −x
3. Calculate each of these derivatives.
d 2
(a) ln[sin(x )]
dx
2
d x
(b) ln
dx x − 1
d sin(e )
x
(c) e
dx
d
(d) sin(ln x)
dx
4. Calculate each of these integrals.

x dx [Hint: Guess p(x) · e
(a) e −x 3 −x ,p a polynomial.]