Week 2

Question 1

Domain?

Answer 1

-all sets of values they give

Question 2

Codomain?

Answer 2

-described by function, outputs not inputs

Question 3

Range?

Answer 3

-values emitted using domain

Question 4

Function?

Answer 4

-emits unique values

𝑓:𝐴→𝐵 where 𝑓(𝑥)∈𝐵 for every 𝑥∈𝐴

Question 5

Surjective?

Answer 5

-codomain = range

Question 6

Injective (one to one)?

Answer 6

• if every horizontal line intersects the graph of f at most once

Question 7

Bijective?

Answer 7

-both surjective and injective

Question 8

How do you prove something is differentiable?

Answer 8

• left and right-hand derivatives are FINITE and EQUAL

Question 9

Differentiating from right?

Answer 9

lim ε->0+ f(x) - f(x+ε) / ε

Question 10

Differentiating from left?

Answer 10

lim ε ->0+ f(x+ε) - f(x) / ε

Question 11

Taylor series?

Answer 11

f(0) + f’(0)(x-a)+f’‘(0) +1/2! f’’‘(0)(x-a)^2 ……