Question

4. Show that $\sin x \approx x$ with an error less than 0.021 for $0 < x < \frac{\pi}{2}$, and with an error less than 0.0002 for $0 < x < 0.1$. Hint: Use theorem (14.3) and note that the \"next\" term is the $x^3$ term. 5. Show that $1 - \cos x \approx \frac{x^2}{2}$ with an error less than 0.003 for $|x| < \frac{\pi}{3}$.

          4. Show that $\sin x \approx x$ with an error less than 0.021 for $0 < x < \frac{\pi}{2}$, and with an error less than 0.0002 for $0 < x < 0.1$. Hint: Use theorem (14.3) and note that the \"next\" term is the $x^3$ term.
5. Show that $1 - \cos x \approx \frac{x^2}{2}$ with an error less than 0.003 for $|x| < \frac{\pi}{3}$.

4. Show that sin x ≈ x with an error less than 0.021 for 0 < x < (π)/(2), and with an error less than 0.0002 for 0 < x < 0.1. Hint: Use theorem (14.3) and note that the n̈extẗerm is the x^3 term.
5. Show that 1 - cos x ≈(x^2)/(2) with an error less than 0.003 for |x| < (π)/(3).

Added by Donna A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Leon Druch

08/26/2021

Step 1

021 for 0 < x < π/2. Show more…

Show all steps

Thanks for your feedback!

4. Show that sin(x) is less than 0.021 for 0 < x < π/2 and with an error less than 0.0002 for 0 < z < 0.1. Hint: Use Theorem 14.3 and note that the next term is the term. 5. Show that 1 - cos(r) ≤ √2 with an error less than 0.003 for 0 < r < π/4.