Post Number Twenty Nine

This week when we actually had a full calculus class we took ap tests. I’m assuming we did corrections in class Friday but I was not there so I only got back the non-calculator portion. I’ll talk about some of those problems later..

First, I’m going to type the Riemann sums formulas because I have yet to remember them!

The Riemann sums approximate the area using the rectangles or trapezoids. The Riemanns Sums are:

LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
*delta x=b-a/number of subintervals

I understand exactly how to take implicit derivatives but for some reason I never get to right answer..

Implicit Derivatives:
take derivative like normal, of both sides of the equation.
any derivative taken for y, mark with dy/dx behind it.
solve for dy/dx

PVA
Position
Velocity
Acceleration
When moving down the list, take a derivative (down-derivative), while when moving up the list, integrate!

I don’t know how to do problems with the constant K or whatever..all help with that will be appreciated.

I also need some refreshment on average value, I thought I knew how to do those but apparently not.

I still need help with integration, especially with trig functions. And I don’t know how to do anything with trig functions being squared..

Some specific problems I’m having are:

Problems when you have to like draw triangles and such to find values.
Problems that ask if f is continuous.

Problems that you need to take a derivative of something like x^2 (square root of 3x+1)

Instantaneous rate of change..

e + 1 S 2 (4/x – 1) dx

And of course plenty more.
I need a tutor… good night everyone!