Final answer:
The limit of f(x) as x approaches -2 does not exist.
Step-by-step explanation:
The function given is f(x) = {sin(x^2)e^x - 2x < -2, -2 <= x}. We are asked to find the limit of f(x) as x approaches -2.
When x is less than -2, the function is sin(x^2)e^x. When x is greater than or equal to -2, the function is -2.
To find the limit as x approaches -2, we need to evaluate the left-hand limit and the right-hand limit separately.
For the left-hand limit, when x approaches -2 from the left side, the function becomes sin((-2)^2)e^(-2) = sin(4)e^(-2).
For the right-hand limit, when x approaches -2 from the right side, the function remains -2.
Since the left-hand limit is sin(4)e^(-2) and the right-hand limit is -2, the limit of f(x) as x approaches -2 does not exist.