{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math151PopSolsII

Math151PopSolsII - MATH 151 POP QUIZ II SOLUTIONS REVIEW...

This preview shows pages 1–3. Sign up to view the full content.

MATH 151 POP QUIZ II: SOLUTIONS REVIEW FOR CHAPTER 10 Find the following limits. Write or - • when appropriate. If a limit does not exist, and and - • are inappropriate, write “DNE” (Does Not Exist). 1) lim x x x Æ - - Æ Æ 3 2 9 3 0 0 As x approaches 3, both the numerator and the denominator approach 0. We have the indeterminate form 0 0 at x = 3 . (Indeterminate forms require further analysis on our part.) The “Factoring and Canceling” trick works here. lim lim lim x x x x x x x x x x x x x Æ Æ Æ - - = + ( ) - ( ) - - ( ) π = + ( ) = = + = 3 2 3 3 9 3 3 3 3 3 3 3 3 3 3 6 We can cancel the factors, because we can assume that if we are considering a limit as approaches 3. We can plug in now. Note: The graph of f x x x ( ) = - - 2 9 3 looks like the graph of g x x ( ) = + 3 , except that there is a removable discontinuity at x = 3 (note that f is undefined there).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2) lim x x x Æ - - Æ Æ 0 9 3 0 0 Again, we have the indeterminate form 0 0 . We will do some preliminary manipulation of the given expression; you sometimes have to do this when trig expressions are involved.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

Math151PopSolsII - MATH 151 POP QUIZ II SOLUTIONS REVIEW...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online