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1. Warmup question: What is the largest value that I sin(0) may take? 2. Let f(x) = sin(2x + 1). The goal of this problem is to estimate the value of the definite 2.0 integral sin(2x + 1) dx using the trapezoidal rule. Follow the directions below. 1.5 (a) Find the second derivative f"(x). Make sure you carefully use the chain rule as you differentiate twice. (b) Using part (a) and #1, find an upper bound K for the second derivative on [1.5,2.0]. Explain your reasoning. (c) Use the theorem for error analysis of the trapezoidal rule to determine how many trapezoids are necessary to estimate the integral within 10-4. (d) Create a spreadsheet that computes In where n is the determine in the previous part. Make sure your spreadsheet is reasonably formatted and includes headers and labels.

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