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# Tutor profile: Lash T.

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Lash T.
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## Questions

### Subject:Pre-Calculus

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Question:

Given the polar coordinates (3, pi/2), find the rectangular coordinates.

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Lash T.

### Subject:Calculus

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Question:

What is the limit as x approaches 0 of (cos2x - 1)/x ?

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Lash T.

The first step in finding a limit is to simply plug in the value that you are approaching. If you plug in 0 for all values of x, you see that cos2(0) -1 is 0, and the denominator is simply 0 since you plugged 0 in for x. This means you found that the limit as x approaches 0 is 0/0. Great news! This means it can most likely be solved by using l'Hopital's rule. To use l'Hopital's rule, start by looking at the numerator. Ignore the denominator for now. The numerator is cos2x - 1. You start by taking the derivative of this entire function, leaving you with -2sin2x [don't forget to use chain rule!]. Set the answer for the numerator aside, and now do the same thing with the denominator. The denominator for your original limit is just x, so the derivative of x is 1. Now you have -2sin2x for the numerator and 1 for the denominator. By l'Hopital's rule, you may now use this as your new limit. Try taking the limit as x approaches 0 of (-2sin2x)/1. Stuck? Pretend that this is your new problem, and forget the original problem that was given to you for now. What is the first step when trying to solve a limit? Plugging in! Plug 0 in for all values of x, and you see that (-2sin[2{0}])/1 ---> (-2sin)/1 ---> (-2)/1 ---> 0/1 = 0. Your answer is lim x-> 0 (cos2x - 1)/x = 0!

### Subject:Algebra

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Question:

What is the "order of operations", how does it work, and why is it important?

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Lash T.

The "order of operations" is as follows: parentheses, exponents, multiplication/division (multiplication and division can be done in any order after parentheses and exponents), and addition/subtraction (similarly, these two can be done in any order after parentheses, exponents, multiplication, and division). A great way to remember this is by using the phrase "Please excuse my dear Aunt Sally" to remember PEMDAS, which is the acronym for the order of operations! When given a math problem, you must start by looking for any parentheses. If you see parentheses, solve whatever is in the parentheses. If you do not see parentheses, move on to the next step, which is looking for any exponents. Continue this process all the way through addition and subtraction, and you will find your answer! If you do not follow the "order of operations", you might get a wrong answer. You may be tempted to answer the problem from left to right, but this is often the incorrect way of solving the problem. For example, 3 + (2 x 6 - 4) should give you 11, but you may get 20 or another result if you do not apply "PEMDAS" correctly.

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