Recall the bounds of the sine function.

Hey Eniola, good to see you again. Here's how to solve the limit problem using the Squeeze Theorem: Step 1: Recall the bounds of the sine function. We know that the sine function is always bounded between -1 and 1, regardless of its argument. -1 ≤ ((1)/(x)) ≤ 1 Step 2: Multiply all parts of the inequality by x^2. Since x^2 ≥ 0 for all real x, multiplying by x^2 does not change the direction of the inequalities. -x^2 ≤ x^2 ((1)/(x)) ≤ x^2 Step 3: Take the limit as x 0 for all three parts of the inequality. We evaluate the limits of the bounding functions: _x 0 (-x^2) = -(0)^2 = 0 _x 0 (x^2) = (0)^2 = 0 Step 4: Apply the Squeeze Theorem. Since _x 0 (-x^2) = 0 and _x 0 (x^2) = 0, and our function x^2 ((1)/(x)) is "sandwiched" between them, the Squeeze Theorem states that the limit of the middle function must also be 0. 0 ≤ _x 0 x^2 ((1)/(x)) ≤ 0 Therefore, _x 0 x^2 ((1)/(x)) = 0 Drop the next question! 📸