# Question 1- Find the second‑order Taylor formula for 𝑓(𝑥,𝑦)=(9𝑥+8𝑦)^2 at x0=(0,0). Note that ℝ2(0,𝐡)=0 in this case. (Use symbolic notation and fractions where needed. Give your answer in the form of 𝑓(ℎ1,ℎ2)=f(l,m) where l=h1 and m=h2.) Answer: 𝑓(𝑙,𝑚)= 2-Find the second‑order Taylor formula for 𝑓(𝑥,𝑦)=8sin(𝑥𝑦)+2cos(𝑥𝑦) at (0,0). (Use symbolic notation and fractions where needed. Give your answer in the form of 𝑓(ℎ1,ℎ2)=𝑓(𝑙,𝑚) where l=h1 and m=h2.) Answer: 𝑓(𝑙,𝑚)=f(l,m)= ....... + ℝ2(0,𝐡) 3-Let 𝑔(𝑥,𝑦)=7sin(𝑥𝑦)−9(𝑥^2)ln(𝑦)+8.. Find the degree 2 polynomial, 𝑝, which best approximates 𝑔 near the point (𝜋2,1). (Use symbolic notation and fractions where needed.) Answer: 𝑝(𝑥,𝑦)= 1- Find the second‑order Taylor formula for 𝑓(𝑥,𝑦)=(9𝑥+8𝑦)^2 at x0=(0,0). Note that ℝ2(0,𝐡)=0 in this case.

(Use symbolic notation and fractions where needed. Give your answer in the form of 𝑓(ℎ1,ℎ2)=f(l,m) where l=h1 and m=h2.)

2-Find the second‑order Taylor formula for 𝑓(𝑥,𝑦)=8sin(𝑥𝑦)+2cos(𝑥𝑦) at (0,0).

(Use symbolic notation and fractions where needed. Give your answer in the form of 𝑓(ℎ1,ℎ2)=𝑓(𝑙,𝑚) where l=h1 and m=h2.)