lecture13

# lecture13 - f c exists(iii lim x → c f x = f c A function...

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

Math 006 (Lecture 13) Indeterminate Form Example 1. Find (a) lim x →- 2 x 2 - 4 x + 2 (b) lim x →- 1 x | x + 1 | x + 1 Deﬁnition 1. If lim x c f ( x ) = lim x c g ( x ) = 0, then lim x c f ( x ) g ( x ) is said to be indeterminate . Theorem 1. If lim x c f ( x ) = L 6 = 0 and lim x c g ( x ) = 0 , then lim x c f ( x ) g ( x ) does not exist. Example 2. Evaluate each of the following limits: (a) lim x 1 x - 1 x 2 - 1 (b) lim x 1 ( x - 1) 2 x 2 - 1 (c) lim x 1 x 2 - 1 ( x - 1) 2 . 1

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

View Full Document
Limit of a Diﬀerence Quotient A limit of the diﬀerence quotient is lim h 0 f ( a + h ) - f ( a ) h . Example 3. Find lim h 0 f ( a + h ) - f ( a ) h when (a) f ( x ) = 4 x - 5, a = 3 (b) f ( x ) = | x + 5 | , a = - 5 and a = 0 (c) f ( x ) = x , a = 2 2
Continuity Deﬁnition 2. A function f is continuous at the point x = c if (i) lim x c f ( x ) exists (ii)
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( c ) exists (iii) lim x → c f ( x ) = f ( c ). A function is continuous on the interval a < x < b if it is continuous at each point on the interval. Example 4. Discuss the continuity of the function f at x =-1 , , 1 and 2. Example 5. Discuss the continuity of each function at the indicated point(s). (a) f ( x ) = x + 1 at x = 1 (b) g ( x ) = x 2-4 x-2 at x = 2 (c) h ( x ) = √ x at x =-1 (d) k ( x ) = | x | x at x = 1 (e) j ( x ) = x 1 3 at x =-1. 3...
View Full Document

## This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

### Page1 / 3

lecture13 - f c exists(iii lim x → c f x = f c A function...

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

View Full Document
Ask a homework question - tutors are online