This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS E MANUEL G OMEZ Solutions Homework 5. Please show all your work. (1) (5 Points) Consider the function f ( x ) = | x | . (a) (3 Points) Compute lim h - f ( h )- f (0) h and lim h + f ( h )- f (0) h . Solution: Lets start by recalling that the function absolute value is defined by | h | = braceleftbigg h if h ,- h if h < . Lets compute first lim h - f ( h ) f (0) h . In this case h , thus h < 0 and therefore | h | =- h . With this in mind we have lim h - f ( h )- f (0) h = lim h - | h |- | | h = lim h - | h |- | | h = lim h - | h | h = lim h -- h h = lim h - (- 1) =- 1 . Similarly, to compute lim h + f ( h ) f (0) h we have h + , thus h > 0 and therefore | h | = h and lim h + f ( h )- f (0) h = lim h + | h |- | | h = lim h + | h | -| | h = lim h + | h | h = lim h + h h = lim h - (1) = 1 . (b) (2 Points) Use the above to conclude that f (0) does not exist even though f is continuous everywhere....
View Full Document
This note was uploaded on 01/20/2012 for the course CALC AS.110.106 taught by Professor Josegomez during the Fall '11 term at Johns Hopkins.
- Fall '11