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calc1 math180 spring 04 exam

# calc1 math180 spring 04 exam - Problem 3(20 pts Let f x = x...

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Math 180 - 8 AM Hour Exam 1 2/20/2004 Name: SSN: Section (circle one) : 8 AM (Xu) 9 AM (Brydges) 10 AM (Brydges) Show all of your work. No work means no credit! All work and solutions should be put on the paper provided. Problem 1: (10 pts) Give a formula for a function which has the following graph. Problem 2: (20 pts) A diﬀerentiable function f ( x ) has the following values given by the table x - 2 0 2 4 6 8 f ( x ) 2 10 16 20 22 21 a) Using the data from this table, make a table of the approximate values of the derivative function f 0 ( x ) for the same values of x . b) Is f ( x ) increasing or decreasing on the interval - 2 x 8? Explain your answer. c) Using the data from your answer to part a), make a table of the approximate values of the second derivative function f 00 ( x ) for the same values of x . d) Is f ( x ) linear, concave up, or concave down on the interval - 2 x 8? Explain your answer.
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Unformatted text preview: Problem 3: (20 pts) Let f ( x ) = x 3 + x . Calculate f (2) using the limit deﬁnition of the derivative . Problem 4: (20 pts) Given the function f ( x ) = ± x 2 + x + 1 if x ≥ 1 3-x if x < 1 (a) State the domain of the function. (b) Determine lim x → 1-f ( x ). (c) Determine lim x → 1 + f ( x ). (d) Is f ( x ) continuous on its domain? Explain your answer. Problem 5: (20 pts) Let f ( x ) = 3 x 2-3 x 2-4 . a) What are the zeros of f ( x )? b) Find all asymptotes for f ( x ). c) Made a careful graph of y = f ( x ). Be sure to label the axes, label the zeros and indicate all asymptotes. Problem 6: (10 pts) Suppose that f (2) =-5 and f (2) = 3. Write the formula for the tangent line to f at x = 2. Return this copy of the exam with your solutions....
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