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With C4 then the 'scope input resistor makes the average output 0VDC and it can swing up to about +1.5V and swing down to about -1.5V.
The output of the LM358 is not symmetrical like most opamps. With a 5.0V supply, an output coupling capacitor and a high load resistance, its output typically goes up to about +1.4V and down to about -2.4V.With C4 the scope shows quiescent output at 0V, and a maximum swing up to +1.6xV and down to -2.2xV, with clipping at both extremes. Does that indicate something wrong with my implementation?