Answer to Question #170544 in Real Analysis for Prathibha Rose

Question

About how.much will the function f(x,y) =ln√(x²+y²) change if the point (x,y) is moved from(3,4) a distance 0.1 unit straight toward (3,6)?

Answer 1

Solution

When point (x,y) moves from (3,4) toward (3,6) only coordinate y is increased starting from 4. So for distance 0.1 unit coordinates of the point are (3, 4.1).

f(3,4) = 1.609, f(3,4.1) = 1.625

Therefore ∆f = f(3,4.1) - f(3,4) = 0.016.

Answer

∆f = 0.016