дz a) yz = ln(x+z) ах 2²u b) u = √√r² + s², r = y + xcost, s = x + y sin t дху c) z = 4ex Iny, x = ln(u cos v), y = u siny zat (u, v) =(2, π/4). ди

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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Question
Q₁: Find indicated partial derivatives
3
əz
a) yz = ln(x+z)
ах'
b) u = √√r² + s², r = y + xcost, s = x + y sin t
a²u
axy
c) z = 4ex Iny, x = In(u cos v), y = u sin yozat (u, v) = (2, 7/4).
ди
Q2: Find the linear approximation of the function of the function f(x, y) = ln (x - 3y)
at (7, 2), then use it to approximte f(5.9, 2.06).
3: The dimensions of a rectangular box are measured to be 75 cm, 60 cm, and 40 cm,
and each measurement is correct to within 0.2 cm. Use differentials to estimate the
largest possible error when the volume of the box is calculated from these
measurements.
Transcribed Image Text:Q₁: Find indicated partial derivatives 3 əz a) yz = ln(x+z) ах' b) u = √√r² + s², r = y + xcost, s = x + y sin t a²u axy c) z = 4ex Iny, x = In(u cos v), y = u sin yozat (u, v) = (2, 7/4). ди Q2: Find the linear approximation of the function of the function f(x, y) = ln (x - 3y) at (7, 2), then use it to approximte f(5.9, 2.06). 3: The dimensions of a rectangular box are measured to be 75 cm, 60 cm, and 40 cm, and each measurement is correct to within 0.2 cm. Use differentials to estimate the largest possible error when the volume of the box is calculated from these measurements.
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