When writing, which sources should I cite?
Any source that you use in researching your work should be cited. It's best to directly quote a source in your writing so that you can cite it clearly on a "works cited" page, however if you do research that you do not actually quote, but that influences your writing, you should cite it on a "works considered" page to ensure that you do not have any plagiarism in your work.
How important are letters of recommendations to the private universities that require them?
In many cases, this is your chance to show your personality to the university you're applying to. The honest opinions of those who have closely worked with you will be taken into account in order to determine how well you would fit in on a certain campus, and if the admissions office had to choose between two students with the exact same test scores, grades, and level of personal statement, they will choose the student that has the most promising letter of rec. Choose who you ask to write your letters carefully.
find: lim ([3(x+h)^6 + 15(x+h)^3 - 7(x+h)] - [3x^6 + 15x^3 - 7x]) / h x--> 0
= 18x^5 + 45x^2 - 7