Consider the sequence of functions $f_t\colon [0,1]^2\rightarrow\mathbb{R}$ defined by
$f_t(x_1,x_2)=x_1x_2(1+\alpha(1-x_1^{1/t})(1-x_2^{1/t}))^t.$
Here $-1\leq\alpha\leq 1$ is a constant. Then $f_t$ converges pointwise to $x_1x_2$. My question is, if it also converges uniformly?