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)

Given that𝑓(𝑥)=2𝑥−3 and 𝑔(𝑥)=1−𝑥4solve (𝑓∘𝑔−1)(𝑥)=(𝑓∘𝑔)(𝑥).

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

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.

Q1. Let 𝐴 = {0,1,2,3,4,5,6,7} suppose 𝑅 𝑎𝑛𝑑 𝑇 are two relations on 𝐴 such that 𝑅 = {(𝑥, 𝑦): 𝑥 + 2𝑦 ≥ 4}, 𝑇 = {(𝑥, 𝑦): 2𝑥 + 3𝑦 ∈ 𝐴} Write 𝑅, 𝑇, 𝑎𝑛𝑑 𝑅°𝑇

If lim𝑥→2𝑓(𝑥)=3𝑥 and lim𝑥→2𝑔(𝑥)=4𝑥2−5, what is lim𝑥→2𝑔(𝑓(𝑥))?