(a) Find (b) Use your answer to part (a) to derive the approximation for near 0. (c) Use
Chapter 1, Problem 126(choose chapter or problem)
Approximation
(a) Find \(\lim \limits_{x \rightarrow 0} \frac{1-\cos x}{x^{2}}\).
(b) Use your answer to part (a) to derive the approximation \(\cos x \approx 1-\frac{1}{2} x^{2}\) for x near 0.
(c) Use your answer to part (b) to approximate cos (0.1).
(d) Use a calculator to approximate cos (0.1) to four decimal places. Compare the result with part (c).
Text Transcription:
lim_x rightarrow 0 1 - cos x / x^2
cos x approx 1 - 1/2 x^2
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