Consider the function f(x, y) = (ex − x)cos y. Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 4) in the direction in which f decreases most rapidly. (Round your components to two decimal places.) $$4.18i−4.08j

-4.18i+4.08 j

Explanation:

We are given that

We have to find the a vector which is perpendicular to the level curve of f through the point in the direction in which f decreases most rapidly.

Grad f(x,y),

Grad f(x,y) at point (2,4) is given by

Hence, the vector which is perpendicular to the level curve of f through the point in the direction in which f decreases most rapidly=-4.18i+4.08 j

ι вєℓιєνє ιт ιѕ тнє fιяѕт ¢нσι¢є(α.)

нє ѕнσυℓ∂ ѕмιℓє ρσℓιтℓу αи∂ ѕρєαк тσ тнє ρєяѕσи ωнσ ιѕ ιитєяяυριиg αfтєя тнє ∂ιѕ¢υѕѕισи

нσρє ι ¢συℓ∂ нєℓρ.