Calc 2 Homework
Jessia Adachi
The proof of planetary motion can be observed through careful observations and calculations made by astronomers over centuries. The laws of motion and gravity, as proposed by Isaac Newton, also provide a solid framework for understanding planetary motion.
One of the key pieces of evidence for elliptical orbits is Kepler's laws of planetary motion, which describe the shape and speed of planets' orbits around the sun. Additionally, observations of planetary positions over time have shown that they do not follow a perfectly circular path, but rather an elliptical one.
Gravitational pull is the force that keeps planets in orbit around the sun. The larger the mass of an object, the stronger its gravitational pull. In the case of planetary motion, the sun's massive gravitational pull keeps the planets in their respective orbits.
Yes, with the help of mathematical equations and advanced technology, planetary motion can be predicted with a high degree of accuracy. However, there are still some factors that may affect the accuracy of these predictions, such as the gravitational pull of other celestial bodies.
Planetary motion is not entirely constant. According to Kepler's laws, planets move at varying speeds and their orbits can also change slightly over time due to gravitational interactions with other objects in the solar system. However, these changes are generally small and can be predicted and accounted for in calculations.
Techniques of integration, exponential growth and decay,separable differential equations, improper integrals, infinitesequences and series, polar coordinates, areas in polarcoordinates, geometry of space, and quadric surfaces.
The syllabus that went into effect Fall 2022 has not changed."Math 212 Syllabus and Homework Effective Spring 2024" documentbelow has been updated for use with the current textbook. Itconsists of three parts:
Second, a supplementary set of suggested homework problems whichare not from the text. The supplementary problem numbers arepreceded by an "s." For example, in the suggested homework problemsfor Section 7.2, the entry s1 refers to supplementary problem7.2/s1.
For the convenience of students who have access to the Thomas'sCalculus: Early Transcendentals, the "Math 212 Syllabus andHomework End After Fall 2023" pdf for that text has been kept toprovide additional exercises. Copies of both the 14th and 15thedition will be placed on reserve at both the NAC library and theMarshak library.
All of the suggested problems from that text are in both the14th and 15th editions, usually with the same number. If the 14thand 15th edition numbers for a problem are different, the listingshows, for example, 53(51), that the problem is listed as number 53in the 15th edition and number 51 in the 14th edition. Informationabout online homework problems will be included when available.
Math 212 (4 hours/4 credits) replaced Math 202 (4 hours/3credits) as part of a plan to replace the previous calculussequence consisting of Math 201, 202, 203 and part of 392 with athree semester sequence. This version of Math 212 was changed,effective Fall 2022, to make it comparable to Calculus II in otherCUNY schools. Vectors, parametric equations and the introduction tomultivariate functions were deleted from the syllabus, andexponential growth and decay, separable differential equations andareas using polar coordinates were added.
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