Find the linearization L(x) of the function at a.f(x) = cos(x), a = 3𝜋/2

The linearization of a function f(x) at a point a is given by the formula:

L(x) = f(a) + f'(a)(x - a)

Here, we are given the function f(x) = cos(x) and the point a = 3π/2.

Step 1: Find f(a) Substitute a = 3π/2 into f(x) to find f(a): f(a) = cos(3π/2) = 0

Step 2: Find f'(x) The derivative of cos(x) is -sin(x), so f'(x) = -sin(x).

Step 3: Find f'(a) Substitute a = 3π/2 into f'(x) to find f'(a): f'(a) = -sin(3π/2) = -(-1) = 1

Step 4: Substitute f(a) and f'(a) into the linearization formula L(x) = f(a) + f'(a)(x - a) = 0 + 1*(x - 3π/2) = x - 3π/2

So, the linearization L(x) of the function f(x) = cos(x) at a = 3π/2 is L(x) = x - 3π/2.

The linearization of a function f(x) at a point a is given by the formula:

L(x) = f(a) + f'(a)(x - a)

Here, we are given f(x) = cos(x) and a = 3π/2.

Step 1: Find f(a) Substitute a = 3π/2 into f(x) to get f(a). f(a) = cos(3π/2) = 0

Step 2: Find f'(x) The derivative of cos(x) is -sin(x). So, f'(x) = -sin(x).

Step 3: Find f'(a) Substitute a = 3π/2 into f'(x) to get f'(a). f'(a) = -sin(3π/2) = 1

Step 4: Substitute f(a) and f'(a) into the linearization formula L(x) = f(a) + f'(a)(x - a) = 0 + 1*(x - 3π/2) = x - 3π/2

So, the linearization L(x) of the function at a = 3π/2 is L(x) = x - 3π/2.