{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

SurCalNotesCh2Sec1and2

# SurCalNotesCh2Sec1and2 - Survey of Calculus 2.1 Fall 2002...

This preview shows pages 1–3. Sign up to view the full content.

Survey of Calculus Fall 2002 Smith 1 2.1 Limits and Continuity Limits There are basically three ways to evaluate limits: (1) _____________________ (2) _____________________ (3) _____________________ I. Evaluating limits graphically . A. The limit of f(x) as x approaches a certain number, c, is the ____________________ that the function gets “___________________” (i.e., the y-value “gets closer to”) as x gets “close to” c (from both sides). Note: The limit of function is NOT the same as the functional value! Example: Consider the graph of 3 3 2 ) ( 2 = x x x x f . (You will need to put the hole in the graph. I can’t get my computer to do it for us. Do you remember where it belongs from College Algebra?) x y -4 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 5 Notice that as x gets “closer to” 3 from both sides, the y-value gets “closer to” ___________. This means that the limit of f(x) as x approaches 3 is ______________. B. Notation: is read as “the limit of f(x) as x approaches c equals L”. In the example above, L x f c x = ) ( lim ) ( lim 3 x f x = ____________. C. If the limit of a function exists, it must be a single real number. Otherwise, we say that the limit ______________________________(DNE). We may use the symbols _____ and ________ to indicate that the values of a function become arbitrarily large or arbitrarily small. Note the paragraph on p. 89.

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

View Full Document
Survey of Calculus Fall 2002 Smith 2 One –Sided Limits A. means the y-value that function gets “close to” as x gets “close to” c from the ______________. ) ( lim x f c x B. means the y-value that the function gets “close to” as x gets “close to” c from the _____________.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

SurCalNotesCh2Sec1and2 - Survey of Calculus 2.1 Fall 2002...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online