Math Stuff

Question 1

what is a square root as an exponent?

Answer 1

X^(1/2)

Question 2

What is 1/x as an exponent?

Answer 2

x^-1

Question 3

How do we simplify x^a/x^b

Answer 3

=x^(a-b)

Question 4

What does concave mean?

Answer 4

Peaks at the top, open at the bottom like n

Question 5

What does convex mean?

Answer 5

Shaped like a U

Question 6

Expand (a+b)^2

Answer 6

= a^2+2ab+b^2

Question 7

expand (a-b)^2

Answer 7

a^2-2ab+b^2

Question 8

Expand (a+b)(a-b)

Answer 8

= a^2-b^2

Question 9

Expand (1-b^2)

Answer 9

= (1+b)(1-b)

Question 10

Answer 10

(n-1)h

Question 11

What is the power rule?

Answer 11

f(x)=x^n becomes f’(x)=nx^(n-1)

Question 12

What is the constant rule?

Answer 12

The derivative of a constant is zero.

Question 13

What is the derivative of the sum or difference of two functions?

Answer 13

The sum or difference of their derivatives.

Question 14

Use the product rule to find the derivative of
u(x)v(x)

Answer 14

u(x)v’(x)+u’(x)v(x)

Question 15

Use the quotient rule to find the derivative of
u(x)/v(x)

Answer 15

[u’(x)v(x)-u(x)v’(x)]/[v(x)]^2

Question 16

Use the chain rule to find the derivative of
y(u(x))

Answer 16

(dy/du)*(du/dx)

Question 17

If the derivative of a function is negative, will the curve be concave or convex?

Answer 17

Concave for a negative.

Question 18

If the derivative of a function is positive, will the associated curve be concave or convex?

Answer 18

Convex for positive.

Question 19

What does ln mean?

Answer 19

Natural Logarithm

Question 20

What is a logarithm?

Answer 20

Definition: The logarithm of a positive real number x to the base b, denoted as log_b(x), is the exponent to which the base b must be raised to obtain the number x. In mathematical notation:

log_b(x) = y if and only if b^y = x

Question 21

When the base of a log/ ln is not specified, what do we assume it to be?

Answer 21

for ln: e or 2.71828
for log: 10

Question 22

ln(1) = ?

Answer 22

ln(1) = 0

Question 23

ln(e)=?

Answer 23

ln(e)=1

Question 24

What is the product rule with regards to ln?

Answer 24

ln(xy) = ln(x) + ln(y)

Question 25

What is the quotient (division) rule for ln?

Answer 25

ln(x/y) = ln(x) - ln(y)

Question 26

What is the change of base formula with regards to both ln and log?

Answer 26

log_b(x) = (log_c(x)) / (log_c(b))
same for ln

Question 27

Use the chain rule to find the derivative of
y(u(x))

Answer 27

(dy/du)*(du/dx)

Question 28

e = ?

Answer 28

e = 2.71828

Question 29

What does this symbol mean?

Answer 29

Nash Equilibrium

Question 30

If we have the function Y=H^(1/2) then what can we say about the relationship of Y to H?

Answer 30

The rate at which Y increases will drop as H gets larger - i.e. decreasing returns to scale.

Question 31

What does FOC mean?

Answer 31

First Order Condition, which is where we set the first derivative to zero, and there may be other constraints on the equation. It specifically has to do with optimization.

Question 32

Is e/2 a term or a constant for the purposes of a derivative of f?

Answer 32

a constant, and therefore gets eliminated.

Question 33

Is a^2ez a constant or a term for the purposes of a derivative of f?

Answer 33

This would be a term and should remain.