{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm_sol

# midterm_sol - Midterm 1 of Math 254.01(Au10 12:30pm-1:18pm...

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

Midterm 1 of Math 254.01 (Au10) October 18, 2010 The Ohio State University 12:30pm-1:18pm Including the cover sheet, this exam consists of seven (7) pages and six (6) problems and is worth a total of 100 points. The point value of each problem is indicated. To obtain full credit, you must have the correct answers along with relevant supporting work to jus- tify them. Partial credit will be given based on the work that is shown. However, answers without sufficient supporting work will receive no credit. Also, you must complete the exam in 48 minutes. Good luck! Name: Signature: OSU Internet Username: Problem # Score Problem # Score 1 4 (15 pts) (18 pts) 2 5 (12 pts) (20 pts) 3 6 (15 pts) (20 pts)

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

View Full Document
1. (a) (5) Calculate lim ( x,y ) (0 , 0) 5 x 2 y x 4 + 4 y 2 , if it exists, or show that the limit does not exist. Solution: Along the curve C 1 : y = 0 , 5 x 2 y x 4 + 4 y 2 = 0 for all ( x, y ) 6 = (0 , 0) . Hence 5 x 2 y x 4 + 4 y 2 0 = L 1 as ( x, y ) (0 , 0) along C 1 . On the other hand, along the curve C 2 : y = x 2 , 5 x 2 y x 4 + 4 y 2 = 5 x 4 x 4 + 4 x 4 = 1 for all ( x, y ) 6 = (0 , 0) . Hence 5 x 2 y x 4 + 4 y 2 1 = L 2 as ( x, y ) (0 , 0) along C 2 . Since L 1 6 = L 2 , lim ( x,y ) (0 , 0) 5 x 2 y x 4 + 4 y 2 does not exist. (b) (2) Is the function f ( x, y ) = 5 x 2 y x 4 + 4 y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) continuous? Justify your answer.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}