11. (5 pts) Let

For questions 1 and 2, refer to the graph of y = f(x) shown below.     1. (6 pts) For each value of a, find: the limit of f(x) as x approaches a from the left the limit of f(x) as x approaches a from the right the limit of f(x) as x approaches a f(a) a) a = -4 b) a = 2 c) a = 4     2. (4 pts) Use the same graph as in #1. Find the three x-values at which f(x) is discontinuous. For each one: a) Using concepts of limits, explain (briefly – a few words) why the function is discontinuous at this value. b) Classify the discontinuity as removable, jump, or infinite. You do not have to explain.

13. (7 pts) A rectangular area adjacent to a river is to be fenced in, but no fencing is required on the side by the river. The total area to be enclosed is 102,900 square feet. Fencing for the side parallel to the river is $7 per linear foot, and fencing for the other two sides is $6 per linear foot. The four corner posts cost $15 apiece. Find the minimum cost of the fence and the dimensions that give this cost. Your answer must include: a drawing definitions of variables the domain of your cost function verification that you have found a minimum value instead of a maximum value

18. (4 pts) Function f(x) is graphed below.     For each statement, say whether it is true or false. Then, explain briefly why you chose your answer. a) This function is differentiable at

4. (4 pts) Let  

PLEASE READ: Here, again, is the link to the Desmos scientific calculator. If an equation doesn’t show up correctly, write down the problem as best you can and solve it. I’ll view your Honorlock session to see what you experienced, then will grade on how you solved the problem you wrote down. If an image is broken, note that on your paper and skip the problem. I’ll view your Honorlock session to verify, then set up a meeting with you to work the problem. When simplifying expressions, you do not have to expand products of polynomials. For example, (7×9 + 3)2  can be left as-is. DO: Collect and simplify like terms Multiply coefficients or variable expressions with the same base (for example, simplify x5 * x3 to x8). You can leave in negative and fractional exponents unless otherwise indicated in a problem.

17. (6 pts) Find the antiderivative F(x) of each function. a)    b)

9. Let     a) (3 pts) Find a linear approximation L(x) for f(x) near x = 9. b) (1 pt) Use your linear approximation to estimate the value of    . Round to 4 places after the decimal. c) (2 pts) Explain why your linear approximation from part a would NOT be a good way to estimate   . Include a drawing in your answer.

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