Question

5. (a) (10 pts) Evaluate the following limit algebraically: $\lim_{x \to 0} \frac{1 - \cos x}{x^2}$ (b) (10 pts) Use your answer from part (a) to show that, for $x$ near 0, we can approximate $\cos x \approx 1 - \frac{x^2}{2}$ (c) (10 pts) Use part (b) to approximate $\cos(0.4)$ to two decimal places $\cos(0.4) \approx$

          5. (a) (10 pts) Evaluate the following limit algebraically: $\lim_{x \to 0} \frac{1 - \cos x}{x^2}$
(b) (10 pts) Use your answer from part (a) to show that, for $x$ near 0, we can approximate
$\cos x \approx 1 - \frac{x^2}{2}$
(c) (10 pts) Use part (b) to approximate $\cos(0.4)$ to two decimal places
$\cos(0.4) \approx$

5. (a) (10 pts) Evaluate the following limit algebraically: limx → 0(1 - cos x)/(x^2)
(b) (10 pts) Use your answer from part (a) to show that, for x near 0, we can approximate
cos x ≈ 1 - (x^2)/(2)
(c) (10 pts) Use part (b) to approximate cos(0.4) to two decimal places
cos(0.4) ≈

Added by Darren L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

05/21/2023

Step 1

To evaluate the limit, we substitute T = -90 into the expression 22. lim T-90 22 = 22 Show more…

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Texts: 1. cos 5. [10 pts] Evaluate the following limit algebraically: lim T-90 22 (b) [10 pts] Use your answer from part (a) to show that, for z near O, we can approximate 2 cosz ~ 1. 10 pt Use the square root to approximate cos0.4 to two decimal places: cos0.4