# Why does Mathematica not evaluate certain simple limits?

Mathematica does not evaluate any of these limits. It seems that the answers should be $1/x$ and $1/y$, respectively.

Limit[(x^k + y^k)^(-1/k), k -> ∞, Assumptions -> x > 0 && y > 0 && x > y]

Limit[(x^k + y^k)^(-1/k), k -> ∞, Assumptions -> x > 0 && y > 0 && x < y]


They seem to be fairly simple limits. Am I missing something here?

• My guess is that Limit treats the expression as a complex-valued function, even though the assumptions imply otherwise. In particular, transformations such as this are not used: PowerExpand[Factor /@ PowerExpand[(x^k + y^k)^(-1/k) /. y -> (u x)]] /. u -> y/x. – Michael E2 May 9 '17 at 22:28
• Limit often fails in cases that seem simple. Try Series instead. – bbgodfrey May 9 '17 at 23:29
• In this case Series performs no better. – bbgodfrey May 10 '17 at 1:27

The limits evaluate for x > 1 && y > 1 for which the larger term dominates
Limit[(x^k + y^k)^(-1/k), k -> Infinity,