(a) Compute the derivative of the function F(x, Y, z) = x² + 2y² – 3z? at the point (1,1, 1) in the direction of v =i+j+k. %D (b) Let f(x,y, z) = xz sin(y). Compute the limit f(1+h, T – h,-1) – f(1,7, –1) -1) – f(1, 7, –1) lim h→0 h

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Complete each of the following.
= x² + 2y? – 3z2 at the point
(a) Compute the derivative of the function F(x,y, z)
(1, 1, 1) in the direction of v = i+j+k.
(b) Let f(x,y, z) = xz sin(y). Compute the limit
f(1+h,
n – h/, -1) – f(1, 7, –1)
V3
lim
h→0
h
(c) Let f(x, y) = e"y. Find the rate of change of f at the point (1,3) in the direction of
the vector that makes an angle of 0 = 37/4 with the x-axis in the xy-plane. What
is the maximum rate of change of f in any direction at this point? Explain.
Transcribed Image Text:Complete each of the following. = x² + 2y? – 3z2 at the point (a) Compute the derivative of the function F(x,y, z) (1, 1, 1) in the direction of v = i+j+k. (b) Let f(x,y, z) = xz sin(y). Compute the limit f(1+h, n – h/, -1) – f(1, 7, –1) V3 lim h→0 h (c) Let f(x, y) = e"y. Find the rate of change of f at the point (1,3) in the direction of the vector that makes an angle of 0 = 37/4 with the x-axis in the xy-plane. What is the maximum rate of change of f in any direction at this point? Explain.
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