Post Number Twenty Eight

I seem to be doing better but I definitely need to memorize some formulas that I should have known a long time ago and such. So here goes nothing..

Riemann Sums:
LRAM RRAM MRAM and TRAM are used for approximations
Uses the interval [a, b], deltax = (b – a)/n
LRAM:
Estimated from the left side, rectangles are drawn from the x-axis and then up to the graph, they then go over.
Deltax [f(a) + f(a + deltax) + … + f(b – deltax)]

RRAM:
Estimated from the right side, rectangles are drawn from the end of the interval of the graph itself.
Deltax [f(a + deltax) + f(b)]

MRAM:
Midpoints of LRAM and RRAM
deltax [f(midpoint1) + f(midpoint2) + f(midpoint n + 1)]

TRAM:
Most accurate of all Riemann sums
deltax/2 [f(a) + 2f(a + deltax) + 2f(a + 2deltax) + … + f(b)]

Tangent Lines:
First take the derivative of f(x)
Then plug in your x to find the slope
Plug x into the original to get your y
After finding your y and your slope, plug into point slope formula:
y – y1 = m(x – x1)

Simple Integration:
There are two types of integration, definite and indefinite.
In definite integration the answer is always a number.
It uses the integral [a, b].
The formula is bSa f(x) dx = f(b) – f(a) = #
Indefinite integration gives you an equation.
All derivative rules apply S x^n dx = x^(n+1)/(n+1) + C

Some things I don’t get are integration problems with square roots and there is an x in front. I have no idea what to do with those.

Also I need help with normal line and bacteria problems.

And I need BIG help with rate of change problems. Ones like find the volume of the cylinder and what not..