To estimate this two-sided limit, we need to examine how the function behaves as x approaches 0 from both directions. Tracing along the curve from the left (negative x-values moving right) and from the right (positive x-values moving left), we see that both paths lead the function values toward y = 1. Since the left-hand and right-hand approaches agree at y = 1, the two-sided limit exists and equals 1. The actual function value at x = 0 might be different or undefined, but this doesn't affect the limit. Students often confuse the limit with the function value, but remember that limits describe approach behavior, not arrival values. For two-sided limits to exist, always verify that both one-sided limits exist and are equal.