Limits of Functions Eric Hoffman Calculus PLHS Sept. 2007

Key Topics L is the limit of the function of f as x approaches a, written: if the values of f(x) approach the unique number L as x approaches a from either direction Look at picture on pg. 95 of book

Key Topics Quadratic Function : the limit of a quadratic function is of the form from this we can see that the limit as x approaches a of a quadratic function f is just the value f(a) Ex. Let f(x) = 3x 2 – 2x + 3 Functions that have the property are called continuous functions

Key Topics Limit of a function that is not continuous: if a function is not continuous it basically means that the function has an asymptote Ex. Let this function is undefined at x=3, so if we want to find the limit of this function at x=3 we can’t just plug 3 in for “a”. This is because the function is not continuous at x=3 To solve we must factor out the “offending” factor

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Limits that don’t exist: If we factor the numerator we notice that (x-3) is not a factor, thus we can’t cancel anything out As x approaches 3 the numerator approaches 6 and the denominator approaches 0 thus the quotient “blows up”

Key Topics Properties of limits: let f and g be functions for which and and let c be any real number. Then: Provided m≠0

Applying the Properties of Limits Find

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Homework pg ,multiples of 3 3,6,9… 8 problems!!