Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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• Problem. Suppose that f(x, y, z) = (1 +x + y² + z³)4 + ln (1+ 3 + 2y + 2).
A. Find the differential
af
af
Əy (2, Y, z) Ay +
(x, y, z) Az
dz
df (x, y, z)
(x, y, z) Ax +
of this function at (x, y, z) = (0,0,0).
B. Use the Linear Approximation Formula
f (x + Ax, y + Ay, z + Az) × f(x, y, z) + df (x, y, z)
and your answer in part A to estimate f(-0.1,0.2,0.1).
C. Evaluate f(-0.1,0.2,0.1) with five decimal places using your calculator and compare that value
with your answer in part B. Is the linear approximation an under, or an over estimate of the actual
function value?
Transcribed Image Text:• Problem. Suppose that f(x, y, z) = (1 +x + y² + z³)4 + ln (1+ 3 + 2y + 2). A. Find the differential af af Əy (2, Y, z) Ay + (x, y, z) Az dz df (x, y, z) (x, y, z) Ax + of this function at (x, y, z) = (0,0,0). B. Use the Linear Approximation Formula f (x + Ax, y + Ay, z + Az) × f(x, y, z) + df (x, y, z) and your answer in part A to estimate f(-0.1,0.2,0.1). C. Evaluate f(-0.1,0.2,0.1) with five decimal places using your calculator and compare that value with your answer in part B. Is the linear approximation an under, or an over estimate of the actual function value?
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