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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Ask a homework question - tutors are online