MATH 1350 Midterm: Math135Exam1Math135Spring2008

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31 Jan 2019
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To get full credit, you must show all work! The exam has 8 problems on 4 pages! Consider the function (a) determine the domain of f . f (x) = x2 1 x2 x 2 (b) find all vertical and horizontal asymptotes of the graph y = f (x). Using the precise ( ) de nition of the limit, prove that lim x 1 (3x + 4) = 1: problem 4. Find the limit lim x (cid:16)x px2 2x(cid:17: problem 5. Consider the function f (x) = x + 2, x2. Determine the points where f is discontinuous, if any. Using the limit de nition of the derivative, nd f (x), where f (x) = x + 3: problem 7. Find the equation of the tangent line to the parabola y = x2 4x + 5 at the point p (1, 2): problem 8.

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