MATH 3A Lecture 3: Math3ALecture3
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MATH 3A Full Course Notes
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Today we will discuss: recap of limit laws, continuous functions define horizontal asymptotes, define vertical asymptotes, tricks to dealing with limits at infinity, non-obvious ways to handle limits. Limit rules: lim f(x) + g(x) = lim f(x) + lim g(x) x x0 lim f(x)g(x) = x x0 x x0 lim f(x) lim g(x)x x0 x x0 x x0 lim f(x) = limx x0 f(x)x x0 g(x) limx x0 g(x) Suppose limx x0 g(x) = l, then lim f(g(x)) = lim f(y)x x0 y l. Using what we"ve seen today, and the previous lecture, how might we evaluate lim sin(x)x . Suppose that f(x) has the property that limx f(x) = l. Then we call l a horizontal asymptote of f(x) if f(x) = l forsome large value of x. Does the function f (x) = 1 + 2x have any horizontal asymptotes? x. Suppose that f(x) has the property that limx x f(x) = ,
