MATH 1A Midterm: MATH 1A Harvard 1a Midterm2 2004 Fall
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7 p. m. - 9 p. m. , science center hall c & e. Instructors: yum-tong siu (course head), peter clark, kim froyshov. 2 ), and f (3). x and h(x) = x 3. Find the natural domains of g f and h f . (hint: refer to your graph!) 1: sketch the graph of f (x) = Are there any removable discontinuities? (re- call: a point is a removable discontinuity if the function f becomes continuous after we change its value at that point. ) x2 1. 2: let f (x) = 3 x x2 2x 8 . Evaluate the following limits. (a) lim x f (x). (b) lim x f (x). (c) lim x 1+ f (x). (d) lim x 1 f (x). (e) lim x 4+ f (x). (f) lim x 4 f (x). 3: compute the derivative of f (x) = x. 4: compute f (x) and f (x) when f (x) = sin2 (x4 + 1).
