13.4 Differentiability and Total Differential by SGLee - YJLim, BYKim
1. Find the total differential of 
when 
.
.
Calculus-Sec-13-4-Solution
13.4 Differentiability and Total Differential by SGLee - YJLim, BYKim
1. Find the total differential of when .
.
2. If 
, find the total differential of 
.
.
3. The base diameter and height of a right circular cone are measured as 10cm and 25cm, respectively,
with a possible error in measurement of as much as 
for each.
Estimate maximum relative error and percentage error in the calculated volume of the right circular cone.
Since the volume of right circular cone is 
,
.
Let 
, then 
.
The maximum relative error is 
and the percentage error is 3.2%.
4. Find an approximation using total differential.
(1) Find an approximation of 
when 
.
(2) Find an approximation of 
.
(1)
.
(2)
Since 
,
.