Calculus II Test 3 7.7-7.8, 8.1, 8.3-8.4, 9.1-9.2 Flashcards Preview

Calculus II > Calculus II Test 3 7.7-7.8, 8.1, 8.3-8.4, 9.1-9.2 > Flashcards

Flashcards in Calculus II Test 3 7.7-7.8, 8.1, 8.3-8.4, 9.1-9.2 Deck (29):
1

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

6

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

11

Newton's Law of cooling

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

12

Exponential

P=C*e^(rt+C)

13

logistic

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

14

Loan

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

15

Convergent sequence notation

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

16

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

17

Squeeze theorem for sequences

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

18

A sequence is increasing if

An+1>An

19

A sequence is decreasing if

An+1

20

A sequence is non-decreasing if

An+1>=An

21

A sequence is non-increasing if

An+1

22

Convergent sequence theorem

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

23

Monotonic sequence

A sequence that is;
increasing
Decreasing
Non-decreasing
Non-decreasing

24

Geometric sequence

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

25

Geometric sequence r=1

r^n-> 1

26

Geometric sequence r=-1

r^n diverges to infinity

27

Geometric sequence r>1

r^n-> infinity

28

Geometric sequence r=-1

r^n diverges

29

Geometric sequence |r| is less than 1

r^n->0