Math 265: 12.1
Supplemental Instruction
IowaStateUniversity
Leader:
Course:
Instructor:
Date:
Trevor
Math 265
Dr. Castillo-Gil
02/09/14
1) Let 𝑓(𝑥, 𝑦) = 𝑥 2 𝑦 + √𝑦. Find each value. What is the domain for
the function?
a. 𝑓(2,1)
b. 𝑓(3,0)
c. 𝑓(1,4)
d. 𝑓(𝑎, 𝑎4 )
𝑦
2) Let 𝑓(𝑥, 𝑦) = + 𝑥𝑦. Find each value. What is the domain for the
𝑥
function?
a. 𝑓(1,2)
1
b. 𝑓 ( , 4)
4
1
c. 𝑓 (4, )
4
d. 𝑓(𝑎, 𝑎)
𝑡
3) Find 𝐹(𝑓(𝑡), 𝑔(𝑡)) 𝑖𝑓 𝐹 (𝑥, 𝑦) = 𝑒 𝑥 + 𝑦 2 and 𝑓 (𝑡) = ln 𝑡 2 , 𝑔(𝑡) = 𝑒 2
4) Sketch the level curves 𝑧 = 𝑘 for the indicated values of k.
𝑥
a. 𝑧 = , 𝑘 = −2, −1,0,1,2
𝑦
b. 𝑧 = 𝑥 2 + 𝑦, 𝑘 = −4, −1,0,1,4
c. 𝑧 = 𝑦 − sin 𝑥 , 𝑘 = −2, −1,0,1,2
5) Various level curve questions out of section 12.1 in the book. I can’t
put the drawings on this sheet!
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