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1 Limit of a Function (Section 2.2) ( ) Question Question Details SCalcET [ ] Explain what is meant by the equation f(x) = 5. x 9 If x 1 9 < x 2 9, then f(x 1 ) 5 f(x 2 ) 5. The values of f(x) can be made as close to 5 as we like by taking x sufficiently close to 9. The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 5. f(x) = 5 for all values of x. If x 1 9 < x 2 9, then f(x 1 ) 5 < f(x 2 ) 5. Is it possible for this statement to be true and yet f(9) = 6? Explain. Yes, the graph could have a hole at (9, 5) and be defined such that f(9) = 6. Yes, the graph could have a vertical asymptote at x = 9 and be defined such that f(9) = 6. No, if f(9) = 6, then f(x) = 6. x 9 No, if f(x) = 5, then f(9) = 5. x 9 1 of 10 2/7/ :49 AM
2 2 of 10 2/7/ :49 AM 2. Question Details SCalcET [ ] Explain the meaning of each of the following. (a) f(x) = x 9 f( 9) = The values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) 9. The values of f(x) can be made arbitrarily close to 9. by taking x sufficiently close to (but not equal to) The values of f(x) can be made arbitrarily close to 9 by taking x sufficiently large. (b) x 7 + f(x) = The values of f(x) can be made negative numbers with arbitrarily large absolute values by taking x sufficiently close to, but greater than, 7. As x approaches 7, f(x) approaches. f(7) = The values of f(x) can be made arbitrarily close to by taking x sufficiently close to Question Details SCalcET [ ]
3 3 of 10 2/7/ :49 AM Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) x 2 f(x) (b) x 2 + f(x) (c) f(x) x 2 (d) f(2) (e) f(x) x 4 (f) f(4) 4. Question Details SCalcET [ ]
4 4 of 10 2/7/ :49 AM For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) x 3 (b) x 3 + (c) x 3 (d) h( 3) (e) x 0 (f) x 0 + (g) x 0 (h) h(0) (i) x 2 (j) h(2) (k) x 5 + (l) x 5 5. Question Details SCalcET [ ]
5 5 of 10 2/7/ :49 AM For the function g whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) t 0 g(t) (b) t 0 + g(t) (c) g(t) t 0 (d) t 2 g(t) (e) t 2 + g(t) (f) g(t) t 2 (g) g(2) (h) g(t) t 4 6. Question Details SCalcET MI.SA. [ ]
6 6 of 10 2/7/ :49 AM This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A patient receives a 150 mg injection of a drug every 4 hours. The graph shows the amount f(t) of the drug in the bloodstream after t hours. Find t 16 f(t) and t 16 + f(t). 7. Question Details SCalcET [ ]
7 Sketch the graph of the function. f(x) = 3 + x if x < 2 x 2 if 2 x < 2 6 x if x 2 Use the graph to determine the values of a for which list.) a = f(x) x a does not exist. (Enter your answers as a commaseparated 7 of 10 2/7/ :49 AM
8 8 of 10 2/7/ :49 AM 8. Question Details SCalcET [ ] Use a table of values to estimate the value of the it. If you have a graphing device, use it to confirm your result graphically. (Round your answer to two decimal places.) x 0 x x 9. Question Details SCalcET [ ] Use a table of values to estimate the value of the it. If you have a graphing device, use it to confirm your result graphically. (Round your answer to two decimal places.) x 7 1 x 1 x Question Details SCalcET MI. [ ] Determine the infinite it. x + 3 x 2 x Question Details SCalcET [ ]
9 9 of 10 2/7/ :49 AM (a) Estimate the value of the it (1 + x) 1/x x 0 to five decimal places. (b) Illustrate part (a) by graphing the function y = (1 + x) 1/x. 12. Question Details SCalcET [ ]
10 10 of 10 2/7/ :49 AM In the theory of relativity, the mass of a particle with velocity v is m 0 m =, 1 v 2 /c 2 where m 0 is the mass of the particle at rest and c is the speed of light. What happens as v c? m m 0 m m m 0 Assignment Details
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