MAT 21A Study Guide - Midterm Guide: Asymptote
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MAT 21A Full Course Notes
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Show your work and explain your reason- ing. If you use a theorem or rule we have seen in class, it may help if you note that in your solution. Problem 1: (10 points) let a, b r, a < b, and suppose that a function f : (a, b) r is de ned for all x in (a, b). State the precise de nition of x b f (x) = . lim: (10 points) use the de nition to prove that lim x 1 . 3: (5 points) lim x 0 sin x . The function f de ned by f (x) = 3x2 + 1 has an oblique asymptote given by the equation y = ax + b: (5 points) find the coe cient a. 5: (5 points) find the constant b, (5 points) sketch a graph of f . Problem 5. (10 points) consider the function f de ned by f (x) =
