To describe a direction, we can make use of the following vector, u = cos(0) i+sin(0) j, 0 < Ꮎ < 27 . Note that u is a unit vector and describes the direction. Assume that the function f in question 2(a) describes the height of a mountain at the position (x, y). Peter is climbing the mountain and his current position is at (5,5). (i) (ii) Find the directions, or equivalently, the range of values of such that if Peter proceeds in those directions, he will be ascending. By writing the directional derivative in the direction of u in terms Vf(5,5) of 0, prove that if Peter proceeds in the direction be ascending at the fastest rate per distance moved. (5,5), he will
To describe a direction, we can make use of the following vector, u = cos(0) i+sin(0) j, 0 < Ꮎ < 27 . Note that u is a unit vector and describes the direction. Assume that the function f in question 2(a) describes the height of a mountain at the position (x, y). Peter is climbing the mountain and his current position is at (5,5). (i) (ii) Find the directions, or equivalently, the range of values of such that if Peter proceeds in those directions, he will be ascending. By writing the directional derivative in the direction of u in terms Vf(5,5) of 0, prove that if Peter proceeds in the direction be ascending at the fastest rate per distance moved. (5,5), he will
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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Kindly solve Part B in the order to get positive feedback please show me neat and clean work for it by hand solution needed
Please do ASAP
Transcribed Image Text:Question 2
(a)
(b)
Consider the two functions of two variables (x,y)
ep(x-2)
у-р
f(x, y) = 5tan-¹ (²) and g(x, y):
where p is a real constant and p = 0, 1. Given that the gradient of f and g are
parallel at the point (2, -1), calculate the possible values of p.
To describe a direction, we can make use of the following vector,
u = cos(0) i+sin(0) j,
0 < Ꮎ < 2.
Note that u is a unit vector and describes the direction.
Assume that the function f in question 2(a) describes the height of a mountain
at the position (x,y). Peter is climbing the mountain and his current position
is at (5,5).
(i)
Find the directions, or equivalently, the range of values of 0 such
that if Peter proceeds in those directions, he will be ascending.
By writing the directional derivative in the direction of u in terms
Vf(5,5)
of 0, prove that if Peter proceeds in the direction
he will
Vf(5,5)'
be ascending at the fastest rate per distance moved.
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