Today’s quiz consisted of several questions centered around finding the area between two curves: \(y=x^2+2x-8\) and \(y = 4-x^2\). The first question asked for the points of intersection for the two curves. By substitution, we arrive at \(x^2+2x-8=4-x^2\) which has solutions \(x=-3\) and \(x=2\). In order to find the points of intersection, we need both \(x\) and \(y\)-coordinates, so for each \(x\) we find the corresponding \(y\). Note that our two \(x\)-values are intersections of the two curves, so both equations should give us the same \(y\)-value when we plug in the same \(x\)-value.
Today’s quiz covered the topic of improper integrals. The first improper integral uses a function, \(f(x) = \frac{2}{\sqrt{x-3}}\), that has a vertical asymptote at \(x=3\). This \(x\)-value is also one of our bounds, which is what makes this an improper integral.
In today’s quiz, we tackle the decomposition of a fraction with a denominator that has both an irreducible quadratic factor (\(x^2+9\)) and a repeated linear factor \((x-3)^2\). Here at the start, it is crucial to make sure that we set up the correct decomposition by noting two important signals: the degree of the denominator and the number of factors.
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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