limits and continuity

Question 1

conditions f(x) is continuous

Answer 1

• lim when x approaches a of f(x) exists
• f(a) exists
• lim when x approaches a of f(x) = f(a)

Question 2

limits at infinity polynomial function

Answer 2

lim┬(𝑥→∞) f(x) = lim┬(𝑥→+/-∞) 𝑎_𝑛 𝑥^𝑛
sign depends on the sign of 𝑎_𝑛

Question 3

limits at infinity rational function

Answer 3

lim┬(𝑥→∞) f(x) = lim┬(𝑥→+/-∞) 𝑎_𝑛 𝑥^𝑛 / b_m x^m
= 0 if n inf to m
= +/- ∞ or -/+ ∞ if n sup to m
= a_n / b_m if n = m

Question 4

continuity of polynomial functions

Answer 4

continuous at every point

Question 5

−∞−∞ =

Answer 5

→−∞

Question 6

((𝑙>0))/(±∞)

Answer 6

→0±

Question 7

((𝑙>0))/(0±)

Answer 7

→±∞

Question 8

(±∞)/((𝑙>0) )

Answer 8

→± ∞

Question 9

(0+)/(±∞)

Answer 9

→0±

Question 10

(+∞)/(0±)

Answer 10

→±∞