Practice Quiz 1c

# Practice Quiz 1c - x = 0? Justify your answer. It may be...

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Practice Quiz IC for Calculus I, MATH 1501 (I) Let f ( x )beg ivenby f ( x )= 1 - x 1+ x for x 6 =0. (a) Find all x such that | f ( x ) - f (1) | < 1. (b) Find a δ ( ± ) > 0 such that | x - 1 | ( ± ) ⇒| f ( x ) - f (1) | <±. and justify your answer. (II) Which of the following limits exist? If they don’t exist, explain why not. If they do, compute the value of the limit. (a) lim x 0 1 x ± 2 2+ x - 2 ² (b) lim x 1 cos ± ( x - 1) 2 ( x 2 - 1) 2 ² (c) lim x →- 2 x 2 +5 x +6 ( x +2) 2 (d) lim x →- 2 ( x 2 +5 x +6) 2 ( x +2) 2 (III): Consider the following function deﬁned for x 6 =0 : f ( x )= 1 x ± 1 x - 1 sin( x ) ² . What value, if any, can be assigned to f (0) to make
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Unformatted text preview: x = 0? Justify your answer. It may be helpfull to recall that x-x 3 < sin( x ) < x for all x > 0. (IV): Consider the sequence given recursively by a n +1 = a 2 n + 1 2 and a 1 = 0 . (a) Is this sequence bounded? If so, give numbers b and c so b a n c for all n . (b) Is this sequence monotone? Expalin your answer. (c) Is this sequence convergent? If so, explain why and compute the limit. If not, explain why not....
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## This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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