00:01
So in this question, they say that the radius and the height of a right circular cylinder are approximately 3 centimeters and 5 centimeters respectively, with an error in measurement of at most 0 .1 centimeters in each.
00:19
Using differentials, i want to estimate what the maximum error in calculating the volume of the cylinder would be.
00:29
So they are telling me that the error in the radius, that's what i call dr, is 0 .1 centimeter.
00:41
While the error in the height, that's what we'll call dh, is also 0 .1 centimeter.
00:51
My goal is to figure out the error in the volume of the cylinder.
01:00
Is to find dv.
01:03
And so first of all, what do i know about the volume of a cylinder? i know that the volume of a cylinder is equal to pi r squared h.
01:14
So i have this function of two variables.
01:19
Now, what do you know about dv if v is a function of r and h? my dv is going to be equal to the partial derivative of v with respect to r times d r plus the partial derivative of v with respect to h times dh.
01:43
And so let's start figuring out those partial derivatives...