limits - x = √ x + 1-1 x × √ x + 1 + 1 √ x + 1 + 1 =...

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

View Full Document Right Arrow Icon
Definition : If f ( x ) becomes closer and closer to a single number L as x gets closer and closer to c from either side, then lim x c f ( x ) = L, which is read as “the limit of f ( x ) as x approaches c is L .” Examples: ( a ) lim x →- 1 3 x 2 + 5 = 3 × ( - 1) 2 + 5 = 8 . ( b ) lim x 2 p x 2 + 1 = p 2 2 + 1 = 5 ( c ) lim x 0 1 x 2 + 1 = 1 0 2 + 1 = 1 . (d) Suppose that f ( x ) = ± | x | x 6 = 0 1 x = 0 . Then lim x 0 f ( x ) = 0 . Note : lim x c f ( x ) relies on the values of f ( x ) at x near c , but may not have any connection to the value of f ( x ) at x = c . Replacement Theorem : If f ( x ) and g ( x ) are equal at all points except for at x = c . Then, lim x c f ( x ) = lim x c g ( x ) Example: x + 1 - 1
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 = √ x + 1-1 x × √ x + 1 + 1 √ x + 1 + 1 = x + 1-1 x ( √ x + 1 + 1) = 1 √ x + 1 + 1 as long as x 6 = 0 (why?). Therefore, lim x → √ x + 1-1 x = lim x → 1 √ x + 1 + 1 = lim x → 1 lim x → ( √ x + 1 + 1) = 1 2 Extra Problems: Find the following limits ( a ) lim x → x 4 + 3 x 3-5 x 2 x , ( b ) lim x → 1 x 2-1 x-1 ( c ) lim x → 1 x-1 x 2-1 ( d ) lim x → 1 x-1 5 x-5...
View Full Document

This note was uploaded on 11/21/2010 for the course MAT 16A 16A taught by Professor Xiao during the Fall '10 term at UC Davis.

Ask a homework question - tutors are online