Consider the function below. lim x -> 3 (2x+1)=7

What values of x guarantee that f(x)=2x+1 is within 0.04 units of 7?

If x is within _____ units of 3, then f(x) is within 0.04 units of 7.
in Calculus Answers by 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

Best answer

Let x=3±h where h is small, then f(3±h)=2(3±h)+1=7±2h, and this must equal 7±0.04.

So we remove 7 from each side, leaving 2h=±0.04, and h=±0.02.

If x is within 0.02 units of 3, then f(x) is within 0.04 units of 7. Strictly, 2.98≤x≤3.02 when 6.96≤f(x)≤7.04.

CHECK

f(3.02)=2×3.02+1=7.04 and f(2.98)=2×2.98+1=6.96. Both 6.96 and 7.04 are within 0.04 units of 7, including the actual values 6.96 and 7.04. 

by Top Rated User (599k points)
selected by

Related questions

Welcome to MathHomeworkAnswers.org, 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!
81,950 questions
86,346 answers
2,238 comments
71,625 users