calc 2 final!

macluarin series of e^x

maclaurin series of cosx

macluarin series of sinx

macluarin series of 1/(1-x)

equals xⁿ

maclaurin series of ln(1+x)

when to use method of washers vs discs for solids of revolution

Discs - no gap between funct and axis ( usually one funct) disc

Washers - gap between funct and axis - if there are two functions bounding the region, there's almost always a gap between one of them and the axis.

formula for area of both circles is just πR²

rotating not around origin ( solids of revolution)

When shifting off axis - radius changes;

Rotating around y = 2, and your function is below it → radius = 2 − f(x)

Rotating around y = −1, and your function is above it → radius = f(x) − (−1) = f(x) + 1

solid of rev by rotating cylinder notes

• cylinder is parallel to axis

• formula is A=2piRH, H is f(x) R is just x, because it changes with bounds of integration ( dont put in fixed radius based on bouns→ leave that to integration portion)
  
  formula for area of cylinder is just πR² H

arc length formula

area of semi circle

½πr²

arc length polar form