Obsolete = no longer used ; completely out of date.

• If a company wants to remain competitive , it should replace all its old and obsolete equipment.
• Old technology is becoming obsolete because of the dramatic pace of development in the field.
• Technological advancements can render some jobs and even the whole industry obsolete.

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Obsolescent = becoming obsolete;  going out of use/fashion.

• The planned obsolescence or built-in obsolescence ( a management terminology used for making a preplanning in such a way that the existing product becomes less attractive with entry of the new product) makes the existing product less attractive by the introduction of the new product with additional functionalities.
• Electronic equipment and gadgets are subject to fast obsolescence.
• Any technology is obsolescent and it is bound to become obsolete one day.