Question

Please do clearly and explain your steps!

13.6 b. Find a normal vector to the level curve corresponding to c = In 5 for the function given by f(x,y)= In(x4 + y^) at the point (-2, 1).

Answer 1

Given f(x,y) = ln (x+y). c=lu s Point (x, y) = (-2,1). f(e,y) = c at P... The usual vector to the level one is the Sadient of the bauction at point. I f(x,y) = fx i + fy j. fe (3,9) - (14(7+y)) Apply the differentiation sule [lu (u(x)} = uc; 4'(x) fo (29) x+y² de (279) the came to pay). bermula: de zu = nx"} fa (1-) - et

fg (1,4) - Sony (10 (2-0) Apply differentiation sale Cu Cuco) in wom). 24 fy(x,y) - 2 Jf (014) = fx i+fyi 0f68,5) = ang teleserye at point (-2,2) of(-2,1) - 26-2);+ 2(0) (23+07 (2877612 Of (-2, 1) = -4 it aj The normal vector to the JF (-2, 1) = level alive -4/6 2 . is

Normal vector to the level curve is (-4/5) i+(2/5) j