This week in Calculus we did reviewed mostly, and then we also got an integration worksheet. I never really knew how to do substitution but I started to get a hang of it finally. Hopefully I remember it from now on.. probably not though.
Some easy things that I sometimes don’t always remember and may help:
Product Rule:
You take the derivative of the first and then leave the second as is, then added to the original first and take the derivative of the second.
First derivative test:
The problem will give u a function and you have to take the derivative of that function and solve for the x values. Then you plug those x values into intervals between negative infinity and infinity. Then plug in numbers between those intervals into the derivative to find if the function is a max, min, increasing or decreasing.
Chain Rule:
For a chain rule, you will have a function raised to a power. For example, lets say you have (2x)^3, You have to bring the 3 out in front and then take the derivative of the inside. So you end up with 6(2x)^2.
Tangent line:
If no y value is given, plug the x value into the original function to find the y value. Then take the derivative of the function and plug in the x value to find the slope. Once this is done, plug everything into point-slope form y-y1=slope(x-x1).
I don’t really know how to find area or volume. If anyone can show me an example please do so.
Also I don’t know how to do the problems with K’s.
All help would be appreciated.
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Both area and volume deal with integrals.
ReplyDeleteFor area, it's the integral from one intersection to the other of top minus the bottom.
For volume, it's generally pi times the integral from one intersection to the other of top squared minus bottom squared (if there is a gap or hole and you need to use washers). Otherwise, it's (top-bottom) squared.