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.
asked Jul 28 in Calculus Answers by 1998cm Level 1 User (940 points)

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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. 

answered Jul 28 by Rod Top Rated User (559,680 points)
selected Jul 29 by 1998cm

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