Flashcards in Calculus II Test 3 7.7-7.8, 8.1, 8.3-8.4, 9.1-9.2 Deck (29):

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## Midpoint rule

###
with a given number of intervals, find the midpoint of each and evaluate the function at each midpoint

sum these and multiply the sum by dx

2

## Trapezoid rule

###
with a given number of intervals, evaluate the function at each interval.

divide the first and last value by two

sum the values and multiply by dx

3

## Absolute error

###
Given an approximation c of an exact value x, the absolute error is E=|c-x|

4

## Improper integral from n to infinity

### substitute t for infinity, take the lim as t->infinity, and evaluate the integral

5

## Improper integral from infinity to n

### substitute t for infinity, take the lim as t->infinity, and evaluate the integral

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## Improper integral from -infinity to infinity

###
split into two integrals; one from neg infinity to 0 and another from 0 to infinity

substitute t for infinity, take the lim as t->infinity, and evaluate the integral

7

## improper unbounded integral

###
an integral with finite bounds in which the function is undefined at one of the bounds or somewhere between.

substitute t for the bound, n, where the function is undefined, take the limit as t->n and evaluate the integral.

8

## Initial value problem

### a Differential equation with initial conditions that allow you to solve for the constant

9

## How to solve a separable differential equation

### separate y and other variables and integrate

10

## solution to y'=ky(t)+b

### y=C*e^(kt)-b/k

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## Newton's Law of cooling

### T(t)=C*e^(-kt)+A

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## Exponential

### P=C*e^(rt+C)

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## logistic

### P(t)=k/(1+C*e^(-rt))

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## Loan

### B(t)=Ce^(kt)-b/k

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## Convergent sequence notation

### lim(n->infinity) An=L or An->L as n-> infinity

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## Sequence theorem

### if given a sequence An for n=1 to infinity and a function f satisfying f(n)=a(n) for n greater than or equal to 1. if lim as x->infinity of f(x)=L then lim as n->infinity of An=L

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## Squeeze theorem for sequences

### given three sequences where Aninfinity) An=lim(n->infinity) Cn=L then lim(n->infinity) Cn=L

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## A sequence is increasing if

### An+1>An

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## A sequence is decreasing if

### An+1

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## A sequence is non-decreasing if

### An+1>=An

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## A sequence is non-increasing if

### An+1

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## Convergent sequence theorem

### If the sequence is monotonic and the sequence is bounded( |An|

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## Monotonic sequence

###
A sequence that is;

increasing

Decreasing

Non-decreasing

Non-decreasing

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## Geometric sequence

### A sequence of the form r^n where r is a constant called a ratio

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## Geometric sequence r=1

### r^n-> 1

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## Geometric sequence r=-1

### r^n diverges to infinity

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## Geometric sequence r>1

### r^n-> infinity

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## Geometric sequence r=-1

### r^n diverges

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