Answer:
a = 2
not continuous
Step-by-step explanation:
In order for f(x) to have a limit at 0, f(0) from the left must equal f(0) from the right.
f(0⁺) = f(0⁻)
-2 + a = a sin(0)
-2 + a = 0
a = 2
If f(x) is continuous at x = 0, f'(0) from the left must equal f'(0) from the right.
f(x) = 0 for x > 0, so f'(x) = 0 for x > 0.
f(x) = 2 sin x for x < 0, so f'(x) = 2 cos x for x < 0.
f'(0⁺) = f'(0⁻)
0 = 2 cos 0
0 = 2
f(x) is not continuous at x = 0.
