Question

Let f(x, y, z)=(4 √(2) y cos (x), 4 y² z). The value of the limit

lim _(x, y, z) →(π / 4,5,5) f(x, y, z) is

Answer 1

The value of the limit is (20, 500).

Step-by-step explanation:

To find the value of the limit lim _(x, y, z) →(π / 4,5,5) f(x, y, z), we substitute the given values into the function f(x, y, z)=(4 √(2) y cos (x), 4 y² z).

Substituting π / 4 for x, 5 for y, and 5 for z, we get f(π / 4,5,5) = (4 √(2) *5 *cos (π / 4), 4 *5² *5) = (20√(2) *cos (π / 4), 100 *5) = (20√(2) *((√2)/2), 500) = (20 *1, 500) = (20, 500).

Therefore, the value of the limit lim _(x, y, z) →(π / 4,5,5) f(x, y, z) is (20, 500).