{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz 2

# Quiz 2 - |(1/x-2 |< ± or equivalently 1 2-δ< x< 1 2...

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

Prof. Haiman Math 1A—Calculus Fall, 2004 Quiz 2 solution—version A Name Student ID Number 1. Calculate each limit, if it exists either as a number or as an infinite limit. If the limit doesn’t exist, say so. (a) lim x 2 x 3 - 4 x x - 2 = lim x 2 x ( x + 2)( x - 2) x - 2 = 8 . (b) lim x 1 1 x 2 - 1 doesn’t exist, since 1 / ( x 2 - 1) + as x 1 + , but 1 / ( x 2 - 1) → -∞ as x 1 - . 2. (a) The fact that lim x 1 / 2 1 x = 2 means that for every > 0, there exists a δ > 0 such that some condition holds. State that condition (as it applies to this specific limit). 0 < | x - 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: | (1 /x )-2 | < ±, or equivalently 1 / 2-δ < x < 1 / 2 + δ, x 6 = 1 / 2 implies 2-± < 1 /x < 2 + ±. (b) Find a δ that veriﬁes the required condition if ± = 0 . 1 . To get 1 . 9 < 1 /x < 2 . 1, need 1 / (2 . 1) < x < 1 / (1 . 9), so δ can be any positive number less than or equal to the smaller of 1 / 2-1 / (2 . 1) = 1 / 42 and 1 / (1 . 9)-1 / 2 = 1 / 38, that is, any < δ ≤ 1 / 42. For example, δ = . 02 would do. 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online