JaneLSumner

### Sequences and Convergence
### Jane Lawrence Sumner
### POLS 508
### Dec. 15, 2015

##### Here are the functions that make the thing work. Scroll down for examples.
fxn <- function(x){
  fx <- (x+1)/x  ## function goes here
  return(fx)
}

JaneLSumner

## The Logic Behind Epsilon-Delta Proof (graphically)
## Jane Lawrence Sumner
## TA: POLS 508, Fall 2015


### CAUTION: THIS IS NOT A PROOF. THIS IS NOT RIGOROUS. THIS IS JUST MEANT    ###
### TO SOLIDIFY THE LOGIC BEHIND THE METHOD IN YOUR BRAIN. THIS IS JUST A     ###
### TOY. PLAY AROUND WITH IT. GET THE LOGIC DOWN. THEN SOLVE IT ANALYTICALLY. ###

## (you can ignore this. this function just lets me generate the same

JaneLSumner

#Understanding the Mean Value Theorem
#POLS 508, Fall 2015
#TA: Jane Lawrence Sumner


# The Mean Value Theorem states that if the function is continuous on the closed 
# interval and differentiable on the open interval, then there exists a point c 
# at which the tangent to that point is parallel to the secant.

## In other words, there exists a point c such that f'(c)=(f(b)-f(a))/(b-a)

JaneLSumner

## Definite Integral as the Limit of a Riemann Sum: Visualizing the Logic
## Jane Lawrence Sumner
## TA, POLS 508, Fall 2015


#### INPUTS HERE ####
a <- 1                          ## lower bound
b <- 10                          ## upper bound
n <- 20                         ## number of iterations