Chapter 4 definitions

Question 1

Define a deleted neighbourhood

Answer 1

Definition 4.1 Let a ∈ R. An interval of the form (c; d) with c < a < d is called a
neighbourhood of a, and the set (c; d) \ {a} is called a deleted neighbourhood of a.

Question 2

Define the limit of a function

Answer 2

Definition 4.2 (Limit of a function) Let f be a real function, a;L ∈ R and assume
that the domain of f contains a deleted neighbourhood of a, that is, f(x) is defined for all x in a deleted neighbourhood of f.

Then f(x)->L as x->a is defined as:
FILL IN

Question 3

Define the left-hand limit

Answer 3

Let f be a real function, a;L ∈ R and assume
that the domain of f contains an interval (a; d) with d > a, that is, f(x) is defined for all
x in (a; d)

Question 4

Define the right hand limit

Answer 4

Let f be a real function, a;L ∈ R and assume
that the domain of f contains an interval (c,a) with a > c, that is, f(x) is defined for all
x in (c, a)

Question 5

Hint : starts with K

define f(x) -> ∞ as x->a and f(x)-> -∞ as x->a

Answer 5

Check definition 4.5

Question 6

Define f(x) -> L as x->-∞ and f(x) -> L as x->∞

Answer 6

Check def 4.4

Question 7

Define f(x) -> ∞ as x->∞

Question 8

Define f(x) -> -∞ as x->∞

Question 9

Define f(x) -> ∞ as x->∞

Question 10

Define f(x) -> ∞ as x->-∞