Consider the following function. f(x) = ln(1 + 2x), a = 2, n = 3, 1.8 ≤ x ≤ 2.2 (a) Approximate f by a Taylor polynomial with de
gree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) |R3(x)| ≤
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The attached image completes the question.
Answer:
- The part (0, 12000) is constant and the slope is zero
- The part (12000, 38000) is decreasing and slope is negative 0.26.
Step-by-step explanation:
Checking the given graph, we see that
For x = 0 to x = 12,000, the values of y are unchanged. For this, we say it is constant.
The slope here is: 0.85 - 0.85 = 0
For x = 12,000 to x = 38,000, the values of y are decreasing. For this, we say it is negative.
The slope here is: 0.59 - 0.85 = -0.26.
