Problems On Taylor's Theorem

Problems on Taylor's Theorem-1:

4. Expand tan ^-1 y/x about the point (1,1) using Taylor's Theorem upto the second degree terms;

Solutions: The expansion of f (x,y) about (1,1) is given by

Let,

Substitute these value in the expansion of f (x,y), we get

5. Evaluate ex cos y by Taylor's theorem about the point (1,π/4) upto the second degree terms.

Solutions: The expansion of f (x,y) about (1,π/4) is given by

The function and its partial derivatives are evaluated at (1,π/4),