3. The base of the pyramid is a square of sides and the height of the pyramid is h. Use the differential (i.e. linear approximation) to estimate the relative error |AV|/V of the volume of the pyramid V = V(h, s) = when s is measured with 1 % relative accuracy and h (harder to measure!) with 3 % relative accuracy,
3. The base of the pyramid is a square of sides and the height of the pyramid is h. Use the differential (i.e. linear approximation) to estimate the relative error |AV|/V of the volume of the pyramid V = V(h, s) = when s is measured with 1 % relative accuracy and h (harder to measure!) with 3 % relative accuracy,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. The base of the pyramid is a square of sides and the height of the pyramid is h. Use the
differential (i.e. linear approximation) to estimate the relative error [AVI/V of the volume of
the pyramid
1
V = V(h,s) = hs²
when s is measured with 1 % relative accuracy and h (harder to measure!) with 3% relative
accuracy.
Hint: To begin with, the general formula to be used in this exercise is
A f(x, y)| Sfe|· |AT| + |fy|-|Ay.
The notation denotes an approximate inequality whose (relative) accuracy improves when
Ax|, |Ay| → 0, but is not necessary valid, because the estimate only includes the linear part
of the change, i.e. the differential without error terms. There would be equality only in the
form
Af = f (x + Ax, y + Ay) — f(x,y) = faAr+ fyAy+ error term,
|Aƒ| ≤ |fz| · |Ax| + |fy| · Ay| + |error term.
from which follows
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