Consider the function below.

lim x -> 3 x^2=9
What values of x guarantee that f(x) = x^2 is within 0.62 units of 9?
If x is within _____ units of 3, then f(x) is within 0.62 units of 9.
asked Jul 28 in Calculus Answers by 1998cm Level 1 User (940 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Let x=3±h where h is small.

f(3±h)=(3±h)²=9±6h+h²=9±0.62, so ±6h≈0.62 if we ignore h² as being insignificantly small.

So h=0.62/6=0.10 approx.

If x is within 0.10 units of 3, then f(x) is within 0.62 units of 9.

answered Jul 28 by Rod Top Rated User (582,800 points)

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,658 questions
85,896 answers
69,335 users