1. Warmup question: What is the largest value that I sin(0) may take?
Let f(x) = sin(2x + 1). The goal of this problem is to estimate the value of the definite
sin(2x + 1) dx using the trapezoidal rule. Follow the directions below.
(a) Find the second derivative f"(x). Make sure you carefully use the chain rule as you
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
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