Math 1A Midterm 1 2006-9-28 2:00-3:30pm. You are allowed 1 sheet of notes. Calculators are not allowed. Each question is worth 3 marks, which will only be given for correct working and a clear and correct answer in simpiﬁed form. 1. Find the domain of the function g ( x ) = 1 √ x 2-6 x . 2. Sketch the graph of y = x sin( x ) for-2 π ≤ x ≤ 2 π . 3. Sketch the graph of the function f ( x ) = x 3 + 1. Find a formula for its inverse f-1 and sketch the graph of f-1 on the same plot. 4. Determine the inﬁnite limit lim x →0 x-1 x 4 ( x + 3) 5. Evaluate the limit lim x → 2 x 2-4 x 3-8 6. If f ( x ) = x 2 , ﬁnd a number δ so that | f ( x )-1 | < 1 / 2 whenever | x-1 | < δ . 7. Find the numbers at which f is discontinuous, where f is deﬁned by f ( x ) = x + 1 if x ≤ 1, f ( x ) = 1 /x if 1 < x < 3, f ( x ) = √ x-3 if x ≥ 3. 8. What is lim x → + ∞ r 12 x 3
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This note was uploaded on 03/08/2010 for the course MATH 1A taught by Professor Wilkening during the Fall '08 term at Berkeley.