Chapter 7

Question 1

How is differentiation important in business math?

Answer 1

It helps analyze certain changes in a function

Question 2

What is the purpose of integration or integral calculus? 4

Answer 2

-Opposite of differentiation
-Used when only rate of change is known.
-Helps reconstruct OG function
-Calculates total amount of costs or total revenue from marginal values

Question 3

What is the formula to find OG function?

Answer 3

f’(x)= ax^n+ b
f(x)= a/n+1 x^n+1 + bx + C0
Don’t forget to always add C0

Question 4

What are the two main tasks of integral calculus?

Answer 4

1. Find the OG function (integration)
2. Calculate area under a curve:
   If f(x) is continuous on [a,b] , integration helps find the area between f(x) and the axis from a to b

Question 5

What is C0?

Answer 5

The integration constant (fixed cost)
-real number

Question 6

What do you call the number on the top of ∫

Answer 6

Upper interval limit b

Question 7

What do you call the number on the bottom of the ∫?

Answer 7

Lower interval limit a

Question 8

How do you calculate the anti derivative with integrals?

Answer 8

F(b)-F(a)

Question 9

What is the purpose of linear algebra in business math?

Answer 9

To optimize complex trader relationships.
Deals with description, analysis and optimization of linear systems

(In optimization problems, the function has to be linear and the constraints are formed in linear equations and linear inequalities )

Question 10

What are the 3 basic elements of linear algebra?

Answer 10

Matrices, vectors, systems of linear equations

Question 11

What is a matrix and what does it consist of

Answer 11

Rectangular number scheme
m rows and n columns
Also called m x n matrix

Question 12

What is a vector and what can it be?

Answer 12

A row vector or a column vector

Row vector: 1 x n matrix
Column vector: 1 x m matrix
(Kabaliktaran of matrix)

Question 13

What are the numbers in front of the variables x1, x2 called in linear algebra?

Answer 13

Coefficients

Question 14

How can you solve a system of linear equations using linear algebra?

Answer 14

using the Gaussian algorithm

Question 15

Which 3 disciplines is linear systems used in business?

Answer 15

interdependencies
internal performance accounting
input-output analysis

Question 16

Where is linear optimization mainly applied in business?

Answer 16

In business research (operations research) for solving planning and decision problems.

Question 17

What is f(x) in integration?

Answer 17

integrand

Question 18

What is dx in integration?

Answer 18

shows the variable to be integrated

Question 19

What is ∫?

Answer 19

integration sign

Question 20

What is the function F in integration?

Answer 20

the anti derivative of function f

Question 21

What does F(b) represent in integration?

Answer 21

the antiderivative at point x = b

Question 22

What does F(a) represent in integration?

Answer 22

the antiderivative at point x = a.

Question 23

What is the the antiderivative of
∫ 1/x dx?

Answer 23

ln(x)+c

Question 24

What is the the antiderivative of
∫ 1/x +3 dx?

Answer 24

ln (x+3) + c

Question 25

What is the the antiderivative of ∫ 5/x -4 dx?

Answer 25

5 ln (x-4) + c

Question 26

What is the the antiderivative of ∫ e^5x dx?

Answer 26

e^5x/5 + c

Question 27

If integration is performed within a certain interval [a, b], wha do you call it

Answer 27

Definite integration

Question 28

How is integration used in business?

Answer 28

To determine the total cost function from marginal cost/ change in cost

Question 29

Which 2 disciplines is difference and differential calculus used in business?

Answer 29

Business cycles and Growth policy e.g GDP

Question 30

What is the term “time dependence of processes”?

Answer 30

analysis of change of variables over time, considering relationship between variables and time

Question 31

What are the two instruments in the study of “time dependencies”

Answer 31

Difference equation And differential equation

Question 32

What is difference equation?

Answer 32

An equation that captures a discreet time (usually date). The variable change of time is modeled by the difference between certain dates.

Question 33

What is y(t) ?

Answer 33

function of time -shows how the variable y changes between 2 points in time -the difference in time is always one step in time How much money you have at time t

Question 34

What type of numbers are a and b in difference equation?

Answer 34

Positive real numbers

Question 35

What is differential equation?

Answer 35

captures the continuous dependency of time variables by using first derivative

Question 36

What do difference and differential equations describe?

Answer 36

A statement that is being tested. The solution of that statement is a function

Question 37

What kind of numbers are used in difference and differential equations?

Answer 37

Positive real number

Question 38

What kind of number is t in e^t in differential equation?

Answer 38

Positive real number

Question 39

What is y’(t)?

Answer 39

Slope, speed of change how fast your money is changing

Question 40

What is the difference between difference and differential equations?

Answer 40

Difference: discreet time (time moves in steps: days, months) -Used for monthly sales, GDP Differential: continuous time (time flows smoothly: any number) -Used for constant growth, inflation

Question 41

What is the equivalent antiderivative function of f(x) in integration

Answer 41

f(x) = F(x)

Question 42

What is indefinite integral

Answer 42

the set of all antiderivatives to f

Question 43

What do you call a matrix in this form 2x1+ 3x2 + 4x3

Answer 43

System of linear equations With: m (row) equations and n (column) variables 3x3 matrix

Question 44

What is the the antiderivative of ∫ lnx dx?

Answer 44

x ln (x) - x + C

Question 45

What is the the antiderivative of ∫ e^x dx?

Answer 45

e^x +C

Question 46

What types of equations are difference and differential equations?

Answer 46

Functional equations

Question 47

What is x in integration of a cost function?

Answer 47

Quantity produced

Question 48

What is a synonym of simple interest

Answer 48

Straight line interest

Question 49

In which business decisions do you use the equivalence principle?

Answer 49

Investment decisions

Question 50

What are two application areas of financial math discussed in the book

Answer 50

Annuity calculation Amortization calculations

Question 51

What is PMT and FVn?

Answer 51

PMT : constant annual annuity rate FVn: final annuity value