6, 8, 10, 14, pg. 1190

20, 21 pg. 1191

25, pg. 1193

36, 38, 40, pg. 1194

8, 12, 14, pg. 1211

18, 20, 26, pg. 1212

43, pg. 1214

14, 16, 18, 24, pg. 1230

30, 34, pg. 1231

42, 44, pg. 1233

8, 10, 16, 20, 24, pg. 1253

26, pg. 1254

32, 34, pg. 1255

12,14, 16, pg. 1272

22, 24, 30, 32, 34, pg. 1273

8, 12, 18, 22, 28, pg. 1287

30, 34, pg. 1288

44, 48, 50, pg. 1290

8, 10, 12, 16, 18, 22, pg. 1333

24, 26, 34, 36, pg. 1334

44, 46, pg. 1335

8, 10, 12, 14, 16, 20, 22, pg. 1348

26, 28, 34, 36, pg. 1349

42, 44, pg. 1350

54, 56, pg. 1351

8, 10, 12, 20, 22, 26, 30, pg. 1370

32, 34, 38, 40, pg. 1371

8, 10, 12, 16, 18, pg. 1387

22, 24, 26, 28, 30, pg. 1388

46, pg. 1389

8, 10, 12, 14, 16, 18, 20, 26, 28, pg. 1405

32, 34, 36, pg. 1406

39, pg. 1407

42, 44, pg. 1408

Make a robot that goes to a wall infront of it and returns to its original position<

1.\(\displaystyle{\lim_{x \to -3} \frac{x^2-9}{x^2+2x-3}} \)

2.\(\displaystyle{\lim_{h \to 0} \frac{\left( h-1 \right)^3 +1}{h}} \)

3.\(\displaystyle{\lim_{x \to \infty} \frac{\sqrt{x^2-9}}{2x-6}} \)

4. \(\displaystyle{\lim_{x \to 1}\left(\frac{1}{x-1}+\frac{1}{x^2-3x+2}\right)}\)

5. \(\displaystyle{\lim_{x \to \infty} \left(\sqrt{x^2+4x+1}-x\right)}\)

6. \(\displaystyle{\lim_{x \to 0} \frac{\sin\left(x\right)}{x}}\)

7. \(\displaystyle{\lim_{x \to 0}\frac{1-e^x}{x}}\)

8. \(\displaystyle{\lim_{h \to 0} \frac{\left(x-h\right)^3-x^3}{h}}\)

9. \(\displaystyle{\lim_{h \to 0} \frac{\sqrt{x+h}-\sqrt{x}}{h}}\)

10. \(\displaystyle{\lim_{h \to 0}\frac{\frac{1}{x+h}-\frac{1}{x}}{h}}\)

7, 9, 15, 19, 21, pg. 1440

22, 23, 26, pg. 1441

28, 30, pg. 1442

41, 43, 44, pg. 1443

8, 10, 14, 18, pg. 1463

24, 26, 30, 32, pg. 1464

42, 44, pg. 1466

8, 10, 14, 16, pg. 1480

22, 24, 28, 30, pg. 1481

34, 36, pg. 1482

46, 48, pg. 1483

8, 10, 16, 18, pg. 1499

24, 26, 32, 34, pg. 1500

36, 38, pg. 1501

44, 46, pg. 1502

8, 10, 12, 14, 16, 22 pg. 1520

26, 28, 30, pg. 1521

30, 32, 36, pg. 1522

8, 10, 12, 16, 18, 20, pg. 1537

28, 30, 32, pg. 1539

34, pg. 1540

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Consider a planet of mass \(6 \times 10^{24} \textrm{kg}\) and radius \(6 \times 10^3 \textrm{km}\). The planet has a moon with mass \(7 \times 10^{22} \textrm{kg}\) and radius \(2 \times 10^3 \textrm{km}\). The moon travels perpendicular to the line connecting the centers of the planets with a speed of \(v=2 \times 10^3 \textrm{km}\) when it has a distance of \(4 \times 10^5 \textrm{km}\) from the center of mass of the planet. Estimate the distance between the two foci of the orbit. Turn in your code, calculations, and a graph of the moon. (5 points)

Alright let's try to solve this problem with numbers!

This is what a blank numbers document looks like. It's good to put your constants in their own cells. To get a cell to put in numerical numbers you can use the black "123" button to put in numbers and the black "=" button to put in equations.

Once you get everything ready you need to input the equation for acceleration. All accelerations should be from equations. Your initial position and velocity should be numbers from the problem.

The components of position and can be updated using the constant acceleration equations.

The components of velocity and can also be updated using the constant acceleration equations.

You can autofill the cells below your equation. Tap on the cell with the keyboard hidden and click on the option "Cell Actions". Then click on "Autofill Cells". This will let you autofill the cells.

Here's the cell I used to plot the surface of the Earth.

Here's my graph. You can make a graph by clicking on the "+" and navigating to the graph button.

JavaScript LinkHere's my graph using javascript and Chart.js.