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Calculus I group study Mod 1

# Calculus I group study Mod 1 - Calculus I Calculus Early...

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Calculus I Calculus: Early Transcendental Functions , 4th ed., by Ron Larson, Robert Hostetler, and Bruce H. Edwards (Boston: Houghton Mifflin, 2007; ISBN-10: 0- 618-60624-6). Calculus Sunday 2.2 – 44, 2.3 – 48, 2.4 - 24, 2.5 – 16 2.2 #44 Find the limit L. Then find ∂ > 0 such that | ƒ ( x ) – L | < 0.01 whenever 0 < | x – c | < oˆ. lim (-1) x 2 lim f(x) = L x 2 lim f(x) = -1 lim (-1) = -1 x 2 L= -1 Let € > 0 | ƒ ( x ) – L | = |-1-(-1) | ƒ ( x ) – L | = |-1 + 1 | | ƒ ( x ) – L | = 0 < € Therefore ∂ > 0 works! | 2-2 |< € | ƒ ( x ) – L | = < € lim (-1) = -1 x 2 2.3 #48 Find the limit of the function (if it exists). Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result. x 3 + 1 lim ---------- x -1 x + 1 Using the formula a 3 + b 3 = (a+b) (a 2 –ab + b 2 ) x 3 + 1 (x + 1) (x 2 – x +1) lim ---------- = lim ----------------------- x -1 x + 1 x -1 (x + 1) x 3 + 1 lim ---------- = lim (x 2 – x +1) x -1 x + 1 x -1 where we can put in our value lim (x 2 – x +1) = (-1)

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