Math 161
6–25–2009
Problems on Differentials
This is PART OF Problem Set 9. It is due on Tuesday, June 30.
1. Let f(x) = (x+ 2)ex. Use differentials to approximate f(−0.2).
2. f(2) = 4 and f′(2) = 7. Use a linear approximation to approximate f(2.03).
3. f(1) = 9 and f′(x) = 6x4
x2+ 1 . Use a linear approximation to approximate f(1.02).
4. A linear approximation is used to approximate y=f(x) at the point (3,1). When dx = 0.06, dy = 0.72.
Find the equation of the tangent line.
5. Let f(x) = √x4+ 9. Find the exact change ∆yand the approximate change dy produced when xchanges
from 2 to 2.1.
6. Let f(x) = x2+x+ 1. Find ∆f=f(x+dx)−f(x) and df =f′(x)dx.
7. The area of a sphere of radius ris A= 4πr2. Suppose that the radius is measured to be 4 centimeters,
with an error of ±0.1 centimeters.
(a) Use differentials to approximate the maximum error in the area produced by an error in measuring r.
(b) Use the result of (a) to approximate the percentage error in the area.
c
2009 by Bruce Ikenaga 1