Unformatted text preview: x → 1 ( x + 3) = 4 Another of the most common algebraic tricks was used in section 2.1 . Here’s another example: EXAMPLE 2.10 Compute lim x →1 √ x + 52 x + 1 . lim x →1 √ x + 52 x + 1 = lim x →1 √ x + 52 x + 1 √ x + 5 + 2 √ x + 5 + 2 = lim x →1 x + 54 ( x + 1)( √ x + 5 + 2) = lim x →1 x + 1 ( x + 1)( √ x + 5 + 2) = lim x →1 1 √ x + 5 + 2 = 1 4 Occasionally we will need a slightly modiﬁed version of the limit deﬁnition. Consider the function f ( x ) = √ 1x 2 , the upper half of the unit circle. What can we say about lim x → 1 f ( x )? It is apparent from the graph of this familiar function that as x gets close to 1 from the left, the value of f ( x ) gets close to zero. It does not even make sense to...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Limits, lim

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