Find the maximum rate of change of f(x, y)=ln(x2+y2) at the point (-2, 2) and the direction in which it occurs.

Step-by-step explanation:

Maximum rate of change of a function f(x,y) is expressed as the gradient of such function at the given point. Gradient of a function is expressed as;

∇f(x,y) =

Given f(x,y)=ln(x²+y²) at the point (-2, 2)

Hence the maximum rate of range of the function at the point (-2,2) is

To get the direction, we willl use the formula;

From the vector gotten, x = -1/2 and y = 1/2

Since tan theta is negative in the second quadrant, the direction in which it occurs will be 180-45 = 135°

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

damm bro the struggle

step-by-step explanation: