Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))

Evaluate the limit: lim (x -> 0) (x^2)/(sin(x))

Step 1: Understand the limit we want to evaluate: lim (x -> 0) (x^2)/(sin(x)).
Step 2: Recall that as x approaches 0, the value of sin(x) gets very close to x.
Step 3: Rewrite the limit using this knowledge: lim (x -> 0) (x^2)/(sin(x)) is similar to lim (x -> 0) (x^2)/x.
Step 4: Simplify (x^2)/x to get x, so now we have lim (x -> 0) x.
Step 5: As x approaches 0, the value of x also approaches 0.
Step 6: Therefore, the limit lim (x -> 0) (x^2)/(sin(x)) equals 0.

Limit Evaluation – Understanding how to evaluate limits, particularly using the behavior of functions as they approach a specific point.
Sine Function Approximation – Recognizing that sin(x) can be approximated by x for small values of x, which is crucial for evaluating limits involving trigonometric functions.