a) You cannot test a resistor in-circuit unless you are certain that the resistance of the circuit to which the resistor is attached is greater than ten times the resistor being tested.
b) The continuity test that produces an audible tone requires the resistance to be lower than a certain value, about 20 ohms.
Read the instructions for the continuity meter and do not expect it to beep when you are measuring a resistance that is higher than the range it is supposed to beep for.
On Many meters you only get the beep on the Diode test range, is this what you are on? or what resistance range?.
The 'Diode Continuity' range usually tests for forward bias and indicates the volt drop in the forward direction?
Max.
The whole purpose of the continuity function on a multimeter is used to test if there is a low resistance path between the two points that you are probing.
You can use it to test if a component such as a transistor or diode is shorted , or if two traces on a pcb are shorted together .. etc.
The Fluke meter I have, which is a high quality brand in N.A. has two functions on the continuity test.
One: Is as a continuity tester that buzzes if res. is < 25Ω and shuts off if over >250Ω.
Two: Testing semiconductor or Diode, it will show 2.4v in the fwd direction and OL in the reverse, if diode is shorted, then it shows <0.5v.
Max.