MATH113 Midterm: MATH113 Midterm 2011 Fall
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Instructions: books, notes or calculators are not permitted, show all your work, make sure your examination paper has 5 questions. Name: (20 points) (a) find the domain of f if f (x) = x2 4. 8 x (b) find horizontal and vertical asymptotes of f (x) = 1 + x sin x lim x 0 (d) let g(x) = e3x+1f (x2). Find g(cid:48)(2) if f (4) = 1, f(cid:48)(4) = 2 . Name: (20 points) evaluate the limit or explain why the limit does not exist: (a) (b) lim x 0 tan(3x) sin(2x) lim x ( x2 + x + x) Name: (20 points) (a) find all possible values of a and b so that the function. X + 2a, x < 1 ax b, 1 x 2. 4x 4, x > 2 f (x) = is continuous at every x. Justify your answer. (b) di erentiate: f (x) = sin(cos(sin(x3))).
