This exercise is not \"practical,\" but helps you understand the equation f[X +

Question

This exercise is not "practical," but helps you understand the equation f[X + dX] - f[X] = df[X] + epsilon | dX | or f[X + dX] - f[X] df[X]. Consider the function f[x, y] = . Compute f[3, 4] by hand. Compute the general symbolic total differential df = dx + dy Compute the specific total differential df = dx + dy when x = 3 and y = 4. Use the specific total differential to approximate f[2.8, 4.1] using only hand computation. Mathematica finds f[2.8, 4.1] as follows. How accurate is your differential approximation?

Explanation / Answer

a) f(3,4) = sqrt(9+16) = sqrt25 = 5

b) f = sqrt(x^2 + y^2)

df = (2x/sqrt(x^2 + y^2)) dx + (2y/sqrt(x^2 + y^2)) dy

c) (x,y) = (3,4)

=> df = (6/5) dx + (8/5) dy

d) f(2.8,4.1) - f(3,4) = (6/5)*(-0.2) + (8/5)*0.1 = -0.4/5 = -0.08

=> f(2.8,4.1) = 5-0.08 = 4.92

e) f(2.8,4.1) = sqrt(2.8^2 + 4.1^2) = 4.965

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.