Stitz-Zeager_College_Algebra_e-book

2 boyles law at a constant temperature the pressure p

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Unformatted text preview: ns 255 the x-axis at (−1, 0). It should make you uncomfortable plugging x = −1 into the reduced formula for h(x), especially since we’ve made such a big deal concerning the stipulation about not letting x = −1 for that formula. What we are really doing is taking a Calculus short-cut to the more detailed kind of analysis near x = −1 which we will show below. Speaking of which, for the discussion that follows, we will use the formula h(x) = (2x+1)(x+1) , x = −1. x+2 • The behavior of y = h(x) as x → −2: As x → −2− , we imagine substituting a number (−3)(− 3 a little bit less than −2. We have h(x) ≈ (very small1)−)) ≈ (very small (−)) ≈ very big (−) ( and so as x → −2− , h(x) → −∞. On the other side of −2, as x → −2+ , we find that 3 h(x) ≈ very small (+) ≈ very big (+), so h(x) → ∞. • The behavior of y = h(x) as x → −1. As x → −1− , we imagine plugging in a number a bit less than x = −1. We have h(x) ≈ (−1)(very 1small (−)) = very small (+) Hence, as x → −1− , h(x) → 0+ . This means, as x → −1− , the graph is a bit above the point (−1, 0). As x → −1+ , we...
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