Use this definition to prove the following limit. lim x → 0 1 x6 = [infinity] SOLUTION Let M be a given positive number. We want to find a number δ such that if 0 < |x| < δ then 1/x6 > M. But 1 x6 > M ⇔ Correct: Your answer is correct. < 1 M ⇔ |x| < $$ Incorrect: Your answer is incorrect. . So if we choose δ = Incorrect: Your answer is incorrect. and 0 < |x| < δ = , then 1/x6 > M. This shows that 1/x6 → [infinity] as x → 0.