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test20cszypowl2

# test20cszypowl2 - Mathematics 20C Spring 2009 Test 2 Name...

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Unformatted text preview: Mathematics 20C Spring 2009 Test 2 Name: Section: ID: Be sure to show all work. Answers without full justification are worth no credit. Remember that you can often check your answers. You may use a single page of notes, but no other aids are allowed. This test consists of 4 questions. Each question is worth a total of 5 points. 1 /5 2 /5 3 /5 4 /5 ∑ /20 1) Compute the following limits or show that they do not exist. (a) lim ( x,y ) → (0 , 0) ye x − y x . This limit can be computed by separating it into two one-dimensional limits and using l’Hˆopital’s rule on the limit in x . That is lim ( x,y ) → (0 , 0) ye x − y x = lim ( x,y ) → (0 , 0) y e x − 1 x = parenleftbigg lim x → e x − 1 x parenrightbiggparenleftbigg lim y → y parenrightbigg = parenleftbigg lim x → e x − 1 parenrightbigg (0) = (1)(0) = 0 . (b) lim ( x,y ) → (1 ,- 2) x − 1 y + 2 . We can approach (1 , − 2) through the line y + 2 = m ( x − 1) where m is an arbitrary slope. Then, lim ( x,y ) → (1 ,- 2) along y +2= m ( x- 1)...
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test20cszypowl2 - Mathematics 20C Spring 2009 Test 2 Name...

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