If you increase production to an infinitely large level, the average variable cost and the average total cost will merge. Why?
Economics 2030 LSU discussion Forum
Examples
As we look at the effect of the marginal cost on the average total cost and the average variable cost, the marginal cost curve pulls the other curves closer as the level of output increases by one unit at a time. Assuming this increase continues on for an infinite amount, the curves will eventually be brought together as the output increases. With all curves trending to an upward slope as you continue to increase output, a meeting of the U-shaped curves is inevitable. The upward slope is indicative of the law of diminishing marginal productivity.