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University of Michigan *

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Geography

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Oct 30, 2023

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1a) i) 5 Going from the left and the right of F(x) both sides lead towards 5. ii) 5/3 iii)14.5 As x is going to xfinity, it is going in an exponential direction that is getting closer and closer to 14.5. Because the problem stated that the horizontal asymptote is at y=14.5 which is what we are looking for as x increases more and more. iv) 7 bi. 3, No it's not because the function is not defined at Ci. 10 tGoing from the left to right towards 7, we see that the point is getting towards 10. cii. 12 Going from the right to left towards 7, we see that the point is getting towards 12. ciii. DNE Going from both the right and left towards 7, we see that the point is not continuous and does not meet together. Thus, it is undefined. . civ. DNE Since 0 is x. Going from the left or right will still make it 0. So F(x+7) as x goes towards 0 will be F(7) which is undefined at that point. cv. DNE Since 0 is x. Going from the left or right will still make it 0. So F(x^3+7) as x goes towards 0 will be F(7) which is undefined at that point. d) (2x(x-3))/(x(x-3)) 2ai) H(x) increase @ (1,4) (4,6)- On the graph, it is going upwards/increasing at these intervals. Decrease @ (0,1) (4,6)- On the graph, it is going downwards/decreasing at these intervals. Concave up @ (0,1),(6.25,7) Concave down @ (1,6.25) 2bi) 2bii)

Explanation: We first figured out what 6pi is and based on that, I found the corresponding equation. Based on the definition of derivative, we then used that to plug in the equations we had. After simplifying it our answer became the one above. 2biii) 3a) Change Direction @ t=5,7,15,17 Explanation: Since velocity is positive when Smerdis is moving north and negative when moving south, everytime the function crosses the x-axis, Smerdi’s velocity changes from positive to negative or negative to positive, thus changing from north to south or south to north. 3b) Move north in intervals (0,5) (7,15) and (17,20), move south in intervals (5,7) and (15,17) Explanation: Whenever the function is positive, Smerdi is moving north, and whenever the function is negative, Smerdi is moving south. 3c) 5 km/hr, 0.75 km/hr) // 4.5 km/hr, 0.75 km/hr Explanation: 3d) Closer to the ocean because the ocean is in the north part. Based on the graph, she has put more distance towards north than she had towards south. Thus, she should be closer to the ocean than when she started. Explanation: It could be observed in the graph that she is moving toward the north most of the time, only temporarily moving toward the south for 4 minutes ((5-7) and (15-17)). It is safe to assume that she is farther away from the ocean. 3e) Closest to the ocean @ t=7 minutes because of the fact that she has gotten closer to the south from the north, Farthest away from the ocean @ t=11, has cancelled southern distance from the earlier point and made more distance to the north Explanation: The biker only traveled temporarily to the south in the interval (7-11) @ t=7, so it is safe to assume that the bike is traveling more to the north in the rest of the interval, so the biker is closest to the ocean @ t=7. The biker is moving north for the rest of the interval, so it can be safe to determine that the biker is farthest away from the ocean @ t=11. 3f) Closest to the ocean @ t=11 minutes because of the fact that she hasn’t moved toward the north, giving it the initial distance; Farthest away @ t=15, because this is the distance that she rode toward the north without turning to the south Explanation: The biker is moving north in the entire interval (11-15). It can be determined that he had moved more north @ t=15 than t=11

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