Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)

Question

lim x→(1/2)⁺ 6x² tan 𝜋x

Answer 1

We can attempt to directly substitute 1/2 into the function. The only problematic part is the Tan(x) part. As x approach 1/2 from the right, Tan(Pi times x) tends off to negative infinity. So the answer is negative infinity. The 6 times x squared part is just some finite number, but any finite number times negative infinity is negative infinity.