Solution Found!
Change on a line Suppose w = f(x, y, z) and ? is the
Chapter 11, Problem 43E(choose chapter or problem)
Change on a line Suppose w = f(x, y, z) and l is the line r(t) = (at, bt, ct), for \((-\infty<t<\infty\).
a. Find w'(t) on l (in terms of a, b, c, \(w_{x}, w_{y}, \text { and } w_{z}\)).
b. Apply part (a) to find w't) when f(x, y, z) = xyz.
c. Apply part (a) to find w' (t) when f(x, y, z) =\(\sqrt{x^{2}+y^{2}+z^{2}}\)?
d. For a general function w = f(x, y, z), find w"(t).
Questions & Answers
QUESTION:
Change on a line Suppose w = f(x, y, z) and l is the line r(t) = (at, bt, ct), for \((-\infty<t<\infty\).
a. Find w'(t) on l (in terms of a, b, c, \(w_{x}, w_{y}, \text { and } w_{z}\)).
b. Apply part (a) to find w't) when f(x, y, z) = xyz.
c. Apply part (a) to find w' (t) when f(x, y, z) =\(\sqrt{x^{2}+y^{2}+z^{2}}\)?
d. For a general function w = f(x, y, z), find w"(t).
ANSWER:Solution 43E
Change on a line Suppose w = f(x, y, z) and ℓ is the line
r(t) = 〈at, bt, ct〉, for − ∞<t < ∞.
(a)
Step 1 of 3:
In the Question it is giving that w = f(x, y, z) and ℓ is the line r(t) = 〈at, bt, ct〉.
But r(t) = 〈at, bt, ct〉 = 〈x, y, z〉
So, x = at , y = bt and z = ct