Well school is finally over. The only thing that is left is graduation. Hut there are a few things I have learned this past year that will definitely stick with me.
Derivatives
The derivative of simple equations such as x^3+9x^2+7x-3. The derivative is 3x^2+18x+7.
Integrals
S 3x^2+4x-8
=x^3+2x^2-8x
Implicit derivatives
All that you do is take the derivative like normal but of x's and y's but put dy/dx right after where you take the derivative of the y then sove for dy/dx.
Limit rules
1) if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents.
2) If the highest exponent is on the top then the limit is infinity.
3) But if the highest exponent is on the bottom then the limit is 0.
Product rule is copy the first times the derivative of the last plus copy the first times the derivative of the second.
Quotient rule is copy the bottom times derivative of the top minus copy the top times the derivative of the bottom all divided by the bottom squared.
Those are the main things that I have learned that have stuck with me all year and will probably stay with me. Calculus this year has been and interesting experience that will stick with me forever. I wish everyone good luck with everything they do.
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