Evaluate the Limit as x approaches -5. (-2/x+5)

Question

Evaluate the Limit as x approaches -5. (-2/x+5)

Answer 1

If you approach -5 from the negative side (x → -5^-), the limit is +∞.  But if you approach -5 from the positive side (x → -5⁺), the limit is -∞.

Answer 2

The most direct way to evaluate a limit is to plug in the value. In this case, you get -5 + 5 in the denominator, which means it's zero. Dividing by zero always means you get ∞ as your answer -- well, unless you also have a zero on top. In that case, it's indeterminate and more work awaits you.

So: all done! Infinity!