Evaluate the Limit:
lim_x→∞ x tan(1/x)

Explanation of All Options

Option (A): ∞ — Incorrect
Although x increases without bound, tan(1/x) decreases to zero.
Their product approaches a finite value, not infinity.

Option (B): 1 — Correct
By using the identity lim_θ→0 (tan θ/θ) = 1,
the limit evaluates to exactly 1.

Option (C): 0 — Incorrect
The decrease in tan(1/x) is balanced by the increase in x, so the result
does not approach zero.

Option (D): -1 — Incorrect
The expression remains positive for large values of x, so the limit
cannot be negative.