Continuity

Question 1

In order for a function ƒ(x) to be continuous at a point x = c, it must fulfill all three conditions

Answer 1

Condition 1: ƒ(c) exists

Condition 2: lim_x→c ƒ(x) exists

Condition 3: lim_x→cƒ(x) = ƒ(c)

Question 2

Jump discontinuity

Answer 2

lim_x→a^- ƒ(x) ≠ lim_x→a⁺ ƒ(x)

Question 3

Point discontinuity

Answer 3

lim_x→a ƒ(x) ≠ ƒ(a)

Question 4

Removable discontinuity

Answer 4

Occurs when you have a rational expression with common factors in the numerator and denominator. Because these can be canceled, the discountinuity is “removable.”

Question 5

Essential discontinuity

Answer 5

Occurs when the curve has a vertical asymptote.