lecture16hout

lecture16hout - MATH 006 Calculus and Linear...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 006 Calculus and Linear Algebra (Lecture 16) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 13
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline 1 Continuity 2 Continuity Properties 3 Solving Inequalities using Continuity Properties Albert Ku (HKUST) MATH 006 2 / 13
Background image of page 2
Continuity Continuity Given a function f , we say that f is “continuous” if its graph y = f ( x ) is “unbroken”. More rigorously, we have the following definition: Definition A function f is continuous at x = c if 1 lim x c f ( x ) exists; 2 f ( c ) is defined; 3 lim x c f ( x ) = f ( c ). A function is discontinuous at x = c if it is not continous at x = c . A function is continuous on the interval a < x < b if it is continuous at each point on the interval. Albert Ku (HKUST) MATH 006 3 / 13
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Continuity Example Suppose the figure below is the graph of the function f . Discuss the continuity of f at x = - 1 , 0 , 1 , 2 and 3. Albert Ku (HKUST) MATH 006 4 / 13
Background image of page 4
Continuity Solutions According to the graph of f , we have f is discontinuous at x = - 1 because lim x →- 1 f ( x ) = 2 6 = f ( - 1). f is continuous at x = 0 because lim x 0 f ( x ) = 1 = f (0). f
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

Page1 / 13

lecture16hout - MATH 006 Calculus and Linear...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online