Question

For the limit lim₍ₓ,ᵧ₎→₍π,₂₎ eˣʸ 1n(cos(xy)), what is the value of the limit?

Answer 1

The value of the given limit is 1 as (x, y) approaches (π, 2).

Step-by-step explanation:

To find the value of the given limit lim₍ₓ,ᵧ₎→₍π,₂₎ eˣʸ 1n(cos(xy)), we need to evaluate the expression as (x, y) approaches (π, 2).

Substituting the values of x and y into the expression, we get eˣʸ 1n(cos(xy)) = eˣʸ 1n(cos(π*2)) = eˣʸ 1n(cos(2π)).

Since cos(2π) = 1, the expression simplifies to eˣʸ 1n(1). Since 1 raised to any power is still 1, we can conclude that the value of the limit is 1.