Question

If f(x,y) = tan'xy, compute f(0.9,-1.2)approximately.​

Answer 1

Answer:

Step-by-step explanation:

Given  

If f(x,y) = tan'xy, compute f(0.9,-1.2)approximately.  

By taking x = 1, y = 1 then Δx = error in x = 0.9 – 1 = - 0.1

Then Δy = error in y = 1.2 – 1 = + 0.2

We know that

Δf = Δf /Δx Δx + Δf/Δy Δy = y/1 + x^2y^2Δx + x/1 + x^2y^2Δy

   = 1/1 + x^2y^2 (yΔx + xΔy)

  = 1/1 + 1 x 1 (1 x (-0.1) + 1 x 0.2)

 = 1/2 (-0.1 + 0.2)

= 0.05

We know that from Taylor’s series

We get f(x,y) = f(1,1) + (Δx Δf/Δx + ΔyΔf/Δy)

                     = f(1,1) + Δf

                     = tan^-1 + 0.05

                    = 45 deg + 0.05

                   = 0.7853 rad + 0.05

                 = 0.83539

Answer 2

Answer:

Step-by-step explanation: