Don’t mix up limp and slimy. Limp carrots are fixable. Toss them in ice water for an hour. They’ll crisp up like magic. It’s vegetable CPR.
Slimy carrots? Throw them away immediately. That slime is a bacterial party you don’t want to attend. Your fridge will smell like a swamp if you ignore it.
One sniff test is all it takes. If it smells like dirt, you’re fine. If it smells like forgotten gym socks, say goodbye.