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Question 2 (a) (b) Consider the two functions of two variables (x, y) f(x,y)=5 tan '() 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. and ep(x-2) y-p g(x,y) To describe a direction, we can make use of the following vector,

Question 2 (a) (b) Consider the two functions of two variables (x, y) f(x,y)=5 tan '() 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. and ep(x-2) y-p g(x,y) To describe a direction, we can make use of the following vector,

Advanced Engineering Mathematics
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 2 (a) (b) Consider the two functions of two variables (x, y) ¹() f(x,y)=5 tan and g(x, y) = (ii) ep(x-2) y-p 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≤0<2π. 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 such that if Peter proceeds in those directions, he will be ascending. By writing the directional derivative in the direction of u in terms of 0, prove that if Peter proceeds in the direction (5,5), he will Vƒ(5,5) be ascending at the fastest rate per distance moved.
Transcribed Image Text:Question 2 (a) (b) Consider the two functions of two variables (x, y) ¹() f(x,y)=5 tan and g(x, y) = (ii) ep(x-2) y-p 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≤0<2π. 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 such that if Peter proceeds in those directions, he will be ascending. By writing the directional derivative in the direction of u in terms of 0, prove that if Peter proceeds in the direction (5,5), he will Vƒ(5,5) be ascending at the fastest rate per distance moved.
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