Evaluate the limit as x approaches infinity of (3 - 2/x).

Evaluate the limit as x approaches infinity of (3 - 2/x).

• A. 0
• B. 3
• C. 1
• D. -∞

Answer: (B)

When a variable grows without bound, fractions like 1/x disappear in the limit because they shrink to zero. Here, 2/x → 0 as x → ∞, so the expression 3 − 2/x tends to 3 − 0. That gives a limit of 3. The subtracted piece is a small positive amount that gets smaller and smaller, so the value sits just below 3 and climbs toward it. The other options would require 2/x to approach a nonzero number or to diverge, which doesn’t happen here.

When a variable grows without bound, fractions like 1/x disappear in the limit because they shrink to zero. Here, 2/x → 0 as x → ∞, so the expression 3 − 2/x tends to 3 − 0. That gives a limit of 3. The subtracted piece is a small positive amount that gets smaller and smaller, so the value sits just below 3 and climbs toward it. The other options would require 2/x to approach a nonzero number or to diverge, which doesn’t happen here.