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

Question 1

Midpoint rule

Answer 1

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

Question 2

Trapezoid rule

Answer 2

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

Question 3

Absolute error

Answer 3

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

Question 4

Improper integral from n to infinity

Answer 4

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

Question 5

Improper integral from infinity to n

Answer 5

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

Question 6

Improper integral from -infinity to infinity

Answer 6

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

Question 7

improper unbounded integral

Answer 7

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.

Question 8

Initial value problem

Answer 8

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

Question 9

How to solve a separable differential equation

Answer 9

separate y and other variables and integrate

Question 10

solution to y’=ky(t)+b

Answer 10

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

Question 11

Newton’s Law of cooling

Answer 11

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

Question 12

Exponential

Answer 12

P=C*e^(rt+C)

Question 13

logistic

Answer 13

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

Question 14

Loan

Answer 14

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

Question 15

Convergent sequence notation

Answer 15

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

Question 16

Sequence theorem

Answer 16

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

Question 17

Squeeze theorem for sequences

Answer 17

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

Question 18

A sequence is increasing if

Answer 18

An+1>An

Question 19

A sequence is decreasing if

Answer 19

An+1

Question 20

A sequence is non-decreasing if

Answer 20

An+1>=An

Question 21

A sequence is non-increasing if

Answer 21

An+1

Question 22

Convergent sequence theorem

Answer 22

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

Question 23

Monotonic sequence

Answer 23

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

Question 24

Geometric sequence

Answer 24

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

Question 25

Geometric sequence r=1

Answer 25

r^n-> 1

Question 26

Geometric sequence r=-1

Answer 26

r^n diverges to infinity

Question 27

Geometric sequence r>1

Answer 27

r^n-> infinity

Question 28

Geometric sequence r=-1

Answer 28

r^n diverges

Question 29

Geometric sequence |r| is less than 1

Answer 29

r^n->0