This is exercise 5.5.1 of Maclane's book "Categories for the Working Mathematician".
Let $X$ be any category. Prove that the projection $P:X^2 \to X \times X$ sending each arrow $f:x \to y$ to the pair $(x,y)$ creates limits. (Here $X^2$ is the functor category whose domain category has two objects, denoted by $1$ and $2$, and only a morphism between them).
Suppose we are given an (small) indexing category $J$ and a functor $F:J \to X$. I was able to find, for each limiting cone $\tau: (x,y) \to PF$, an element $f: x \to y$ in $X^2$ and a cone $f \to F$. Namely, I took $f:x \to y$ to be the second component of the unique arrow $(x,x) \to (x,y)$ given by the universal property of limit, when considering the cone $(x,y) \to PF$ obtained from $\tau$ by precomposing it with $(id, f_i)$, where in this case $f_i$ is the image of the unique arrow $1 \to 2.$