Starting with problem four on the Final Exam Review sheet, we looked at part a. The region described is bounded by a parabola \(y = x^2-9\) and the \(x\)-axis, \(y=0\). Because the region defines \(y\) as a function of \(x\), this is an indication that we will use \(dx\) rectangles. Because \(dx\) rectangles are vertically oriented, and our axis of revolution is the (horizontally oriented) \(x\)-axis, the two are perpendicular — and we conclude that this situation requires the “disc” or “washer” method.
Today’s quiz consisted of a single problem: find the fifth-degree Taylor Polynomial approximation of the function \(f(x)=\ln(x)\) centered at \(x=1\). In setting up for this Taylor Polynomial, we create a table with rows for all values of \(n\) starting at \(n=0\) and ending at the fifth-degree: \(n=5\).
Today’s quiz contained three questions about arc length. The entire problem consisted of setting up (but not evaluating) the integral for arc length of the given functions. Recall that the arc length of \(f(x)\) from \(x=a\) to \(x=b\) is calculated using the integral: \[L = \int_a^b \sqrt{1+\left[f'(x)\right]^2}\,dx\]
The WeBWorK Q&A site is a place to ask and answer questions about your homework problems. HINT: To ask a question, start by logging in to your WeBWorK section, then click “Ask for Help” after any problem.
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