APPM 1340 Final: appm1340fall2015examfinal_sol_0
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Instructions: books, notes, and electronic devices are not permitted. Write neatly, top to bottom, left to right, one problem per page. A correct answer with incorrect or no supporting work may receive no credit. Therefore, we have points of tangency ( . 12 , 1) on f (x) and g(x). The slopes of the tangent lines are found with f ( . The tangent line equations that we seek are: y = 12x+(2 ) and y = 12x+(1 ). The squeeze theorem can be used to nd the lim g(x) for what values of a and k? x a. Solution: (a) (b) domain is all real numbers. (c) range is [0, ). (d) f (x) = (cid:26) 2(x 2) Solution: (a) f (x) is continuous at x = a if lim x a f (x) = f (a). (b) lim x 0 (cid:20) 3x x2. 5x x2(cid:21) = lim lim x 0+ tan(3x) csc(5x) = lim.
