Question

Consider the following common approximation when \(x\) is near zero. a. Estimate \(f(0.3)\) and give the maximum error in the approximation using \(n = 2\). b. Estimate \(f(0.7)\) and give the maximum error in the approximation using \(n = 2\) \(f(x) = \sin(x) \approx x\) a. \(f(0.3) = \square\) (Type an integer or a decimal)

          Consider the following common approximation when \(x\) is near zero.
a. Estimate \(f(0.3)\) and give the maximum error in the approximation using \(n = 2\).
b. Estimate \(f(0.7)\) and give the maximum error in the approximation using \(n = 2\)
\(f(x) = \sin(x) \approx x\)
a. \(f(0.3) = \square\) (Type an integer or a decimal)

Consider the following common approximation when x is near zero.
a. Estimate f(0.3) and give the maximum error in the approximation using n = 2.
b. Estimate f(0.7) and give the maximum error in the approximation using n = 2
f(x) = sin(x) ≈ x
a. f(0.3) = □ (Type an integer or a decimal)

Added by Marina J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Imogen Dell

Step 1

Estimating âˆš3: When x is near zero, we can use the approximation âˆš(1+x) â‰ˆ 1 + x/2. So, âˆš3 â‰ˆ 1 + 3/2 = 2.5. The maximum error in this approximation using 2 is |âˆš3 - 2.5| = 0.5. Show more…

Show all steps

Thanks for your feedback!

Consider the following common approximation when x is near zero. Estimate âˆš3 and give the maximum error in the approximation using 2. Estimate âˆš0.7 and give the maximum error in the approximation using 2. Find f(x) = sin(x) and give the maximum error in the approximation using 2.