MATH 1350 Midterm: Math135SampleExam1
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Sample exam i math 135, spring 2008. No graphing calculators allowed during exams: problem 1. Find the domain and sketch the graph of the function f (x) = 1 x+3 , using the appropriate transformation: problem 2. Find the limit lim x 3 x2 9 x2 2x 3: problem 3. Prove the statement using the precise ( ) de nition of the limit lim x 2 (5 2x) = 1: problem 4. 3 x, (x 3)2, if x < 0 if 0 x < 3 if x 3. Determine the points where f is discontinuous, if any: problem 5. Find the limit lim x (cid:16)px2 + 4x + 1 x(cid:17) : problem 6. Using the limit de nition of the derivative, nd f (x) where f (x) = State the domain of the function and the domain of its derivative: problem 7.