64 Part I: The Questions
Using Linearizations to
Estimate Values
429– 431 Estimate the value of the given number
using a linearization.
429. Estimate 7.96
2/3
to the thousandths place.
430. Estimate 102 to the tenths place.
431. Estimate tan 46° to the thousandths place.
Understanding Related Rates
432– 445 Solve the related-rates problem. Give an
exact answer unless otherwise stated.
432. If V is the volume of a sphere of radius r and
the sphere expands as time passes, find dV
dt
in terms of dr
dt
.
433. A pebble is thrown into a pond, and the
ripples spread in a circular pattern. If the
radius of the circle increases at a constant
rate of 1 meter per second, how fast is the
area of the circle increasing when the radius
is 4 meters?
Finding and Evaluating
Differentials
423– 425 Find the differential dy and then evaluate
dy for the given values of x and dx.
423. y = x
2
– 4x, x = 3, dx = 1
6
424. y x
=
+
1
1
2
, x = 1, dx = –0.1
425. y = cos
2 
x, x = π
3
, dx = 0.02
Finding Linearizations
426– 428 Find the linearization L(x) of the function
at the given value of a.
426. f
 
(x) = 3x
2
, a = 1
427. f
 
(x) = cos x + sin x, a = π
2
428. f x
x
x
( ) =
+
2
3
, a = 2