Let 𝑓𝑓(𝑖𝑖, 𝑗𝑗) = 𝑖𝑖 𝑗𝑗𝑗𝑗!(a) Calculate 𝑓𝑓(2,3).(b) Calculate ∑ 𝑓𝑓(2, 𝑗𝑗)2𝑗𝑗=0 , ∑ 𝑓𝑓(𝑖𝑖, 3)3𝑖𝑖=1 .(c) Calculate ∑ ∑ 𝑓𝑓(𝑖𝑖, 𝑗

(b) 𝑓 (𝑥 + 𝑖𝑦) = 𝑥3 + 𝑖(𝑦 − 1)3

Find 𝑓𝑥 and 𝑓𝑦 for 𝑓(𝑥,𝑦)=(1+𝑥−𝑦)𝑒𝑥+2𝑦 Question 9Select one: a. 𝑓𝑥=(−1−2𝑥+𝑦)𝑒𝑥+2𝑦,𝑓𝑦=(3−4𝑥+2𝑦)𝑒𝑥+2𝑦. b. 𝑓𝑥=(2+𝑥−2𝑦)𝑒𝑥+2𝑦,𝑓𝑦=(2𝑥−4𝑦)𝑒𝑥+2𝑦. c. None of these d. 𝑓𝑥=(2+𝑥−𝑦)𝑒𝑥+2𝑦,𝑓𝑦=(1+2𝑥−2𝑦)𝑒𝑥+2𝑦. e. 𝑓𝑥=(−𝑥+𝑦)𝑒𝑥+2𝑦,𝑓𝑦=(3−2𝑥+2𝑦)𝑒𝑥+2𝑦.

Evaluate the following.∫(−2𝑥)d𝑥=

𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 𝑎𝑛 𝑚 × 𝑛 𝑚𝑎𝑡𝑟𝑖𝑥 𝐴 𝑡ℎ𝑎𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑠𝑞𝑢𝑎𝑟𝑒? Question 10Select one: 𝑅𝑎𝑛𝑘(𝐴) = 𝑚𝑖𝑛(𝑚, 𝑛) 𝑅𝑎𝑛𝑘(𝐴) ≤ 𝑚𝑖𝑛(𝑚, 𝑛)  𝑅𝑎𝑛𝑘(𝐴) = 𝑚𝑎𝑥(𝑚, 𝑛)𝑅𝑎𝑛𝑘(𝐴) ≥ 𝑚𝑖𝑛(𝑚, 𝑛)

Find 𝑓𝑥𝑥 , 𝑓𝑥𝑦 and 𝑓𝑦𝑦 for the function 𝑓(𝑥,𝑦)=3𝑥2+3𝑥2𝑦2+2𝑥𝑦4+3𝑦3 Question 6Select one: a. 𝑓𝑥𝑥=6+12𝑦2,𝑓𝑥𝑦=12𝑥𝑦+12𝑦3,𝑓𝑦𝑦=3𝑥2+24𝑥𝑦2+12𝑦. b. 𝑓𝑥𝑥=12+6𝑦2,𝑓𝑥𝑦=6𝑥𝑦+12𝑦3,𝑓𝑦𝑦=12𝑥2+12𝑥𝑦2+18𝑦. c. 𝑓𝑥𝑥=6+6𝑦2,𝑓𝑥𝑦=12𝑥𝑦+8𝑦3,𝑓𝑦𝑦=6𝑥2+24𝑥𝑦2+18𝑦. d. 𝑓𝑥𝑥=6+6𝑦2,𝑓𝑥𝑦=8𝑥𝑦+12𝑦3,𝑓𝑦𝑦=6𝑥2+12𝑥𝑦2+12𝑦. e. None of these