show that M isn't close map

Question

the line search map $M:En\times E_n \rightarrow E_n$ defined below is frequently encountered in nonlinear programming algorithm.the vector $y∈ M(x,d)$ if it solves the following problem where $f:E_n \rightarrow E_1 : f(x+ad)$ st $ x+ad \geq 0$ & $a \geq0$. How show that M is not close? . hint a sequence $(x_k,d_k)$ converging to $(x,d)$ & a sequence $y_k∈ M(x,d)$ converging to $y$ must be exhibited such that $y∉ M(x,d)$ . given that $x_1=(0,1), x_k+1$, is a point on the circle $(x_1-1)^2+(x_2-2)^2=1$ midway between $x_k$ and $(0 ,1)$ the vector $d_k$ defined by $ \frac{(xk+1 -xk)}{||xk+1-xk||}$ .letting $f(x_1,x_2)=(x_1+2)^2+(x_2-2)^2=0$ show that a.) the sequence {$x_k$}converges to $(0,1)$ b.the vector {$d_k$} converges to $d=(0,1)$ b.the vector {$y_k$} converges to $y=(0,1)$ d.the map M is not closed.