Limits: if you can’t just plug in the number it approaches (which is when you get a zero on the bottom), you have to manipulate algebra and cancel out anything that can be and then plug in the number. If that doesn’t work, you then can try to use your table function. Then if That doesn’t work, it is DNE.
Optimization: Identify primary and secondary. Solve secondary for 1 variable (if applicable) and plug into primary. Take derivative of primary to solve for other variable and plug into the secondary equation to find the other variable. (Confusing I know…but it’s not that difficult…patience)
Example:
The sum of two numbers is 120. The product of the two is 7200. Find the minimum values
Set up equations: x + y = 240
xy = 7200
Solve the secondary for, let’s pick, y. So, y = 240-x.
Plug into primary
x(240 – x) = 7200
Take Derivative
1(240 – x) + (-1)(x) = 0
Solve for x.
x=120
Plug into when we solved y.
y=120
Simple enough right? So apply that same principle to other problems like when finding dimensions and area.
Related Rates: Everything is in reference to time. You have to be able to identify your formulas and everything that’s given out of words. Get what I’m saying? And remember that speed can’t be negative (made that mistake a few times). Also, don’t forget your units!!!!
Idk if this will be on the AP, but can someone explain percent error again? I vaguely remember it..but you know how those things are...
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