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L08 - Lecture 8 — Limits at Infinity Asymptotes Suppose...

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Unformatted text preview: Lecture 8 — Limits at Infinity, Asymptotes Suppose an observer 5 kilometers from a launching pad watches a rocket rise vertically into the air. What happens to the angle of elevation θ from the observer to the rocket as it rises? Does it have a limiting value? Observe the values of S and T in terms of height H . T = tan( θ ) S = sin 2 ( θ ) What happens to each as H becomes arbitrarily large? So what happens to θ ? We say a function f ( x ) has limit L as x approaches ∞ (-∞ ) if, given any small distance , we can show that the distance between each f ( x ) and L is smaller than , once x is chosen sufficiently large (negatively large). We write lim x →∞ f ( x ) = L or f ( x ) → L as x → ∞ ( x →-∞ ) ( x → – ∞ ) The line y = L is called a horizontal asymptote for the function f if and only if How many horizontal asymptotes may the graph of a function have? How many vertical asymptotes?...
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L08 - Lecture 8 — Limits at Infinity Asymptotes Suppose...

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