11DIFFERENTIATION - Department of Mathematics

Exercises
In Exercises 1–6, use dy to approximate y for
the function y f(x) when x changes from x
a to x b.
1. f(x) 0.21x 7 3.22x 4 5.43x 2 1.42x 12.42; a 3,
b 3.01
2. f(x) 0.2x2 3.1
; a 2, b 1.96
1.2x 1.3
3. f(x) 2.2x 2 1.3x 4; a 1, b 1.03
4. f(x) x2x 3 x 4; a 2, b 1.98
5. f(x) x2 4
; a 4, b 4.1
x 1
6. f(x) 2.1x 2 3
5; a 3, b 2.95
x
7. C ALCULATING M ORTGAGE P AYMENTS Refer to Example 2.
How much more per month will the Meyers’ mortgage
payment be if the interest rate increases from 10% to
10.3%/year? To 10.4%/year? To 10.5%/year?
8. E STIMATING THE A REA OF A R ING OF N EPTUNE The ring
1989N2R of the planet Neptune has an inner radius of
approximately 53,200 km (measured from the center of
the planet) and a radial width of 15 km. Use differentials
to estimate the area of the ring.
9. E FFECT OF P RICE I NCREASE ON Q UANTITY D EMANDED The quantity
demanded per week of the Alpha Sports Watch, x
(in thousands), is related to its unit price of p dollars by
the equation
50 p
x f(p) 10 (0 p 50)
p
Use differentials to find the decrease in the quantity of
the watches demanded per week if the unit price is increased
from $40 to $42.
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