{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

a5 242

# a5 242 - MATH 242 Analysis 1(Fall 2011 Assignment 5 Due in...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 242 Analysis 1 (Fall, 2011) Assignment 5. Due in class Thursday, November 24. Instructions: This assignment is out of 50 points. You may choose any questions whose points add up to 50. As in the previous assignment, provide all details in your work. Also as previously, stars (*) indicate possibly more challenging questions. 1. (10 pts.) (a) If f ( x ) = 1 / √ x, x > 0, use the definition to find f ′ ( x ) for each x > 0. For the following functions on R , find all points where f ′ ( x ) does not exist, and find f ′ ( x ) when it does exist, proving your answers in each case: (b) f ( x ) = x sin(1 /x ) for x negationslash = 0, f (0) = 0, (c) f ( x ) = : x 2 if x is rational, x 3 if x is irrational. 2. (10 pts.) Use the Mean Value Theorem to prove that ( x − 1) /x < ln x < x − 1 when x > 1. [You may assume the facts that the function ln x has derivative 1 /x and − ln x = ln(1 /x ), on x > 0.] 3. (10 pts.) Let f : [ a, b ] → R be continuous on [ a, b ] and differentiable in...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

a5 242 - MATH 242 Analysis 1(Fall 2011 Assignment 5 Due in...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online