Question

Вычислите f(-pi/2).если f(x)=xcosx 

Answer 1

To find f(-pi/2), we need to evaluate the function f(x) = xcos(x) at x = -pi/2.

Plugging in x = -pi/2 into the function, we get: f(-pi/2) = (-pi/2)cos(-pi/2)

Using the product-to-sum identity for cosine, which states that cos(A)cos(B) = (1/2)(cos(A + B) + cos(A - B)), we can rewrite the expression as: f(-pi/2) = (-pi/2)(1/2)(cos(-pi/2 + (-pi/2)) + cos(-pi/2 - (-pi/2)))

Simplifying the expression inside the parentheses: f(-pi/2) = (-pi/2)(1/2)(cos(-pi) + cos(0))

Since cos(-pi) = cos(pi) = -1 and cos(0) = 1, we can further simplify: f(-pi/2) = (-pi/2)(1/2)(-1 + 1)

Finally, simplifying the remaining expression: f(-pi/2) = (-pi/2)(1/2)(0)

Multiplying the numbers together: f(-pi/2) = 0

So, f(-pi/2) is equal to 0.