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Unformatted text preview: Homework # 2 Due: 5/30/06 1. Use the graph to find the following limits: lim f (x) lim f (x) lim f (x) lim f (x) lim f (x) x2+ x0 x2- x2 x-1 2. Sketch the graph of a function that satisfies all of the given conditions: lim f (x) = 1 lim f (x) = 1 lim f (x) = 2 f (0) = 1 x0- x1 x0+ f (x) is undefined 3. Use the limit laws to find the following limits. Justify each step. (a) lim (x2 + 3)(x - 4)
x-3 (b) lim (c) lim x-2 3 x2 x -8 x1 x+ 1 x 6 4. Find the following limits. You don't need to justify each step, but remember to show work. (a) lim (b)
x+3 2 x-3 x -9 lim 1+x-1 x x0 5. Use the Squeeze Theorem to show that
x0 lim x2 sin (1/x) = 0 3x2 + 2 is continuous at x = -5 7. Find an equation of the tangent line to y = 2x + 1 at the point (4,3). 6. Show that f (x) = ...
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- Spring '08