This week we went over another AP test and i actually did a lot better on these compared to my other ones lol... so let's start out with the things i know:
Limit Rules:
When dealing with a limit and it asks what is the limit as x goes to infinity, you are going to use your limit rules:
1. If the degree on top is bigger than the degree on the bottom, the limit is infinity.
2. If the degree on top is smaller than the degree on the botton, the limit is 0.
3. If the degree on top is the same as the degree on the bottom, then you divide their coefficients to get the limit.
If they give you a limit problem and it asks you what the limit is as h goes to 0, then you have to take the derivative of whatever is behind the parenthesis on top of the fraction. This only happens when h is in the problem.
If they asks for the limit as x goes to some number, then you plug that number into the function and see what the answer is.
Another thing that shows up a lot is first and second derivative.
First derivative:
you find if a function is increasing or decreasing and you find max and mins
You take the derivative of the function and solve for x values which are critical values. Then you set those numbers into intervals between negative infinity and infinity. Then you plug those numbers into the derivative to find whatever you need to find.
Second derivative:
you find where the function is concave up or concave down and where there are points of inflection.
You take the derivative of the function twice and find the critical values. Set them up into intervals and plug numbers between those intervals into the second derivative to find what you are looking for.
Things i am still having trouble with(on the AP test we just finished):
1. Number 11 on the non-calculator portion.
2.Number 12 on the non-calculator portion.
3.number 16 on the non-calculator portion.
4. Number 19 on the non-calculator portion.
5. Number 24 and 25 on the non-calculator portion.
6. Number 28 on the non-calculator portion.
7. Number30 and 32 on the calculator portion
8.Number 35,36, and 37 on the calculator portion.
9. Number 41 and 42 on the calculator portion.
10. Number 45 on the calculator portion.
See you all tomorrow :)
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number 19 is Reimann sums. They give you the graph is increasing and concave up so the first step is to sketch the graph. After sketching the graph, draw your sums on the graph. RRAM will start at the right and go to the left (over approximation in this case), LRAM starts from the left and goes right (under approximation), Trapezoidal depends on the graph so if it is increasing, it is over as it is in this case. If it is decreasing, it is under. From there, order your rams. L<M<T<R
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