Lesson03_-_Limits_ws

# Lesson03_-_Limits_ws - x → ln x 2-ln 2 x x 1 01 001 001...

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Worksheet for Section 1.3 The Concept of Limit V63.0121: Calculus I Spring 2010 1. Use the graph of the function f to decide whether the value of the given quantity exists. If it does, find it. If not, explain why. x y - 2 - 1 1 2 3 4 5 - 2 2 3 4 (i) f ( - 2) (ii) lim x →- 2 f ( x ) (iii) f (0) (iv) lim x 0 f ( x ) (v) f (2) (vi) lim x 2 f ( x ) (vii) f (4) (viii) lim x 4 f ( x ) 2. (a) Draw a graph of f ( x ) = x 2 +1 and use it to guess the value of lim x 2 f ( x ). Call this number L . (b) Draw a horizontal strip around y = L . (c) Can you draw a vertical strip around x = 2 which confines the graph of f within the horizontal strip from (b) 1

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(d) Do you think this can be done for every horizontal strip? 3. Complete the table and use the result to estimate the limit lim
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Unformatted text preview: x → ln( x + 2)-ln 2 x . x-. 1-. 01-. 001 . 001 . 01 . 1 ln( x + 2)-ln 2 x 4. Return the function f ( x ) = x 2 + 1. We will argue that lim x → 3 f ( x ) = 10. (a) Find a number d for which f ( x ) is within 1 of 10 whenever x is within d of 3. In other words, ﬁnd a number d such that 9 < f ( x ) < 11 whenever 3-d < x < 3 + d (b) Find a number d for which f ( x ) is within 0 . 1 of 10 whenever x is within d of 3. (c) Find a number d for which f ( x ) is within 0 . 05 of 10 whenever x is within d of 3. 2...
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