Business Calculus Ch1

Front 1

Open intervals

Back 1

The set of numbers that lie stirctly between two fixed numbers a and b is called an open interval (a,b)

Hint 1

It consists of all the real numbers that satisfy the inequalities
a < x < b. It is called “open” because neither of its endpoints is included in the interval.

Front 2

Closed Intervals

Back 2

The set of real numbers that lie between two fixed numbers a and b, that includes a and b, is called a closed interval [a, b].
It consists of all the real numbers that satisfy the inequalities
a < or = x < or = b.

Hint 2

It is called “closed” because both of its endpoints are included in the interval.

Front 3

Half-Open Intervals

Back 3

The set of real numbers that between two fixed numbers a and b, that contains only one of its endpoints a or b, is called a half-open interval (a, b] or [a, b).

Hint 3

It consists of all the real numbers that satisfy the inequalities a < x < or = b or a < or = x < b

Front 4

infinite intervals

Back 4

(a, ∞ ), [a, ∞ ), (–∞ , a), and (–∞ , a].

Hint 4

The above are defined, respectively, by the set of real numbers that satisfy
x > a, x ≥ a, x < a, x ≤ a.

Front 5

Exponents and Radicals

Back 5

If b is any real number and n is a positive integer, then the expression bn is defined as the number

Hint 5

bn = b · b b · · … · b

Front 6

The number b is called the base, and the superscript n is called the power of the exponential expression b to the nth

Back 6

2 to the 5 = 2*2*2*2*2 = 32

Hint 6

2/3 to the 3 = 2/3 * 2/3 * 2/3 = 8/27

Front 7

If b ≠ 0, we define b0 = 1

Back 7

20 = 1 and (–π )0 = 1, but 0 to the 0 is undefined.

Front 8

If n is a positive integer, then the expression b to the 1/n is defined to be the number that, when raised to the nth power, is equal to b, thus

Back 8

( b to the 1/nth) nth = b

Front 9

Such a number is called the nth root of b, also written as

Back 9

n th √ b

Front 10

1 Law

Back 10

am · an = am + n

Hint 10

x2 · x3 = x2 + 3 = x5

Front 11

Squaring numbers in 50s

Back 11

1.)add 25 to ones digit for the first part of the answer
2.)then square the ones digit and tack this on to the end of the first part of the answer
if you end up with a one digit answer put a 0 in front

Hint 11

51*51=
25+1=26
1*1=1
2601= 51*51

Front 12

Squaring two digit numbers that end in 5

Back 12

1.) 25 is the second half of the answer
2.) first part of answer take tens digit of the number you're trying to square and multiply if by the number one greater than it

Hint 12

15*15=
1.) = 25
2.) = 1*2= 2
15*15 = 225

Front 13

Squaring numbers in the 40's

Back 13

1.)Always begin with the # 15 add that to the ones digit for the first part of the answer
2.) how much less than 50 the number is you are squaring and square that answer for the second part of the answer. add a 0 before the number in step two if you get a one digit number

Hint 13

46*46=
15+6=21 = the first part
50-46= 4 and 4*4=16 = the second part
46*46=2116

Front 14

55*55=

Back 14

25+5=30
5*5=25

Hint 14

3025

Front 15

58*58=

Back 15

25+8=33
8*8=64

Hint 15

3364