Stuff.page

<apex:page controller="Thingy">
  This blank canvas with our controller applied lets us invoke the remoting methods from the dev console via:
  <ul>
    <li><code>Thingy.regularLimits(function(response){console.log('Regular limits are:',response);});</code></li>
    <li><code>Thingy.readOnlyLimits(function(response){console.log('Regular limits are:',response);});</code></li>
  </ul>
</apex:page>

Thingy.cls

public class Thingy{
    @RemoteAction
    public static Map<String,Integer> regularLimits(){
    	return getLimitsData();
    }
    
    @ReadOnly
    @RemoteAction
    public static Map<String,Integer> readOnlyLimits(){
    	return getLimitsData();
    }
    
    private static Map<String,Integer> getLimitsData(){
        return new Map<String,Integer>{
            'getLimitCallouts()' => Limits.getLimitCallouts(),
        	'getLimitCpuTime()' => Limits.getLimitCpuTime(),
        	'getLimitDMLRows()' => Limits.getLimitDMLRows(),
        	'getLimitDMLStatements()' => Limits.getLimitDMLStatements(),
        	'getLimitFutureCalls()' => Limits.getLimitFutureCalls(),
        	'getLimitHeapSize()' => Limits.getLimitHeapSize(),
        	'getLimitQueries()' => Limits.getLimitQueries(),
        	'getLimitQueries()' => Limits.getLimitQueries(),
        	'getLimitQueryRows()' => Limits.getLimitQueryRows(),
        	'getLimitScriptStatements()' => Limits.getLimitScriptStatements(),
        	'getLimitSoslQueries()' => Limits.getLimitSoslQueries()
    	};
    }
}