Question

1. Find the equation of the tangent plane to the function f ( x, y ) = x^2 + y^2 at the point (1,1).

2. Find a different solution to Laplace's equation.

Answer 1

(1)

we are given

Firstly, we will find point

we can plug x=1 and y=1

now, we can find partial derivatives

we can plug x=1

we can plug y=1

now, we can use tangent plane formula

we can plug values

we can simplify it

and we get

...........Answer