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Pick a number.  Double it. Multiply the result by 3.  Add 24. Divide by 6. Subtract your original number.  Is the result always the same? Write a convincing argument for your answer.

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Patrina Schowalter
Patrina SchowalterLv2
21 Feb 2019
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Related questions

Write a word problem to match the expression step by step

x/3 = x/4 + 18

-x/4     -x/4

(x/3 - x/4) = 18

*multiply to change the denominators*

(4x/6 - 3x/6) = 18

x/6 = 18

6(x/6) = 6(18)

x = 108

Now we just halve that to get the number

108 ÷ 1/2 = 54

54 is the answer

4. (21 pts) Let g be the function given by ( 6 - X 2 + x if x < 2, x + -2 g(x) = x2 – x-1 if x>2. (a) (6 pts) Use the definition of continuity to determine whether the function g is continuous at 2. Show your work. (b) (3 pts) Evaluate the limit. Justify your answer. Show your work. Write "does not exist" only if the limit does not exist and is not + or -0. lim g(x) = lim -2+ = +00 X 2 + X since the form of the limit is NUM: POS, DENOM: POS (c) (2 pts) Write the equation(s) of all vertical asymptotes of g. Write "none" if appropriate. The result in part (b) implies that the line x= -2 is a vertical asymptote. This is the only vertical asymptote, since the function g is continuous on its domain (d) (2 pts) Determine the largest) intervals of continuity of g. Use interval notation to write your answer. Let g be the function given by 12+ if x < 2, x# -2 2 + x g(x)= x2-x-1 x-1 if x>2. (e) (6 pts) Evaluate each limit. Do not use L'Hôpital's Rule. Write "does not exist" only if the limit does not exist and is not too or -00. Show your work. 6-1 i lim g(x) = lim -00 2 + X = lim -002 + x 0-1 + 1 x -00 x x x -+- 2 +1 0 0 + 11 x2 - x-1 1 ii. lim g(x) = lim x++ V x2 – x-1 X-1 x2 - x-1 X - 1 = lim x +oc x +0 - lim Vam M93001 (f) (2 pts) Write the equation(s) of all horizontal asymptotes of g. Write "none" if appropriate.

4. An erroneous proof of a statement is given below. Indicate where a fundamental error in the argument is made. Briefly explain what the error is. The statement is false but this is not relevant to your answer. The lines of the proof have been labelled to make it easier for you to answer. [2 marks] Statement: Let a and b be positive real numbers. If b > 5, then log, (250) <3. Proof: (1) Let a, b e R where a, b > 0. (2) Assume b>5. (3) Using rules of logarithms, log(250) = logo 25+ logo a. (4) Since b > 5, then log, 25 = logo 52 <2. (5) When a = b, log, a = 1. (6) Therefore logo (25a) < 2+1 = 3.

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