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Suppose f is twice differentiable on an interval I containing the point x = c. Taylor's remainder theorem (we will see this in more detail later) says that |f(x) - L(x)| ≤ M\x-c|² where L is the linear approximation for f at x = c, M is the maximum of f"(x) on I and x is close to C. Using this, determine how many digits of accuracy the linear approximation for f(x) = cos(x) at c = 0 approximates cos(0.02). Assume all units are radians.

Suppose f is twice differentiable on an interval I containing the point x = c. Taylor's remainder theorem (we will see this in more detail later) says that |f(x) - L(x)| ≤ M\x-c|² where L is the linear approximation for f at x = c, M is the maximum of f"(x) on I and x is close to C. Using this, determine how many digits of accuracy the linear approximation for f(x) = cos(x) at c = 0 approximates cos(0.02). Assume all units are radians.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Suppose f is twice differentiable on an interval I containing the point x = c. Taylor's remainder theorem (we will see this in more detail later) says that |f(x) - L(x)| ≤ M\x-c|² where L is the linear approximation for f at x = c, M is the maximum of f"(x)| on I and x is close to C. Using this, determine how many digits of accuracy the linear approximation for f(x) = cos(x) at c = 0 approximates cos(0.02). Assume all units are radians.
Transcribed Image Text:3. Suppose f is twice differentiable on an interval I containing the point x = c. Taylor's remainder theorem (we will see this in more detail later) says that |f(x) - L(x)| ≤ M\x-c|² where L is the linear approximation for f at x = c, M is the maximum of f"(x)| on I and x is close to C. Using this, determine how many digits of accuracy the linear approximation for f(x) = cos(x) at c = 0 approximates cos(0.02). Assume all units are radians.
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