Sec 2 5 Continuity Continuous Function Intuitively any

Sec 2. 5: Continuity Continuous Function Intuitively, any function whose graph can be sketched over its domain in one continuous motion without lifting the pencil is an example of a continuous function.

Sec 2. 5: Continuity at a Point A function f(x) is continues at a point a if Example: study the continuity at x = -1 Continuity Test

Sec 2. 5: Continuity at a Point (interior point) A function f(x) is continues at a point a if Example: study the continuity at x = 4 Continuity Test

Sec 2. 5: Continuity at a Point (interior point) A function f(x) is continues at a point a if Example: study the continuity at x = 2 Continuity Test

Sec 2. 5: Continuity at a Point (interior point) A function f(x) is continues at a point a if Example: study the continuity at x = -2 Continuity Test

Sec 2. 5: Continuity at a Point Cont a A function f(x) is continues at an end point a if Cont from right at a Cont from left at a

Sec 2. 5: Continuity Types of Discontinuities. infinite discontinuity removable discontinuity Which conditions Later: oscillating discontinuity: jump discontinuity

Sec 2. 5: Continuity

Sec 2. 5: Continuity Exam 1 -102

Sec 2. 5: Continuity

Sec 2. 5: Continuity Continuous on [a, b]

Sec 2. 5: Continuity Remark The inverse function of any continuous one-to-one function is also continuous.

Sec 2. 5: Continuity Inverse Functions and Continuity The inverse function of any continuous one-to-one function is also continuous. This result is suggested from the observation that the graph of the inverse, being the reflection of the graph of ƒ across the line y = x

Sec 2. 5: Continuity

Sec 2. 5: Continuity Exam 1 -122

Sec 2. 5: Continuity continuous

Sec 2. 5: Continuity Exam 1 -101

Sec 2. 5: Continuity Geometrically, IVT says that any horizontal line between ƒ(a) and ƒ(b) will cross the curve at least once over the interval [a, b].

Sec 2. 5: Continuity The Intermediate Value Theorem 1) ƒ(x) cont on [a, b] 2) N between ƒ(a) and ƒ(b) N = ƒ(c) c in [a, b]

Sec 2. 5: Continuity One use of the Intermediate Value Theorem is in locating roots of equations as in the following example.

Sec 2. 5: Continuity E 1 TERM-121

Sec 2. 5: Continuity Exam 1 -101