Private Sub Command1_Click()
Dim tolerance, ZetaGuess1, ZetaGuess2, ZetaGuess3, ZetaGuess4, Zeta1, Zeta2, Zeta3, Zeta4, f1, f1d, f2, f2d, f3, f3d, f4, f4d, damping, error As Double
tolerance = 0.00001
h = Val(Text_h.Text)
L = Val(Text_L.Text)
k = Val(Text_k.Text)
bi = h * L / k

'use damping for large bi numbers, but limit damping for large bi numbers
If bi <= 1 Then
    damping = 1
ElseIf bi < 500 Then
    damping = 1 / bi
Else
    damping = 0.001
End If
Label_bi.Caption = bi

'For loop for number of roots
For j = 1 To 4
        Zeta = (j - 1) * (3) + 0.7
    'For loop for iterations of Newton's Method
    Do
        'Newton's Method
        f = Zeta * Tan(Zeta) - bi
        fd = (Sin(Zeta) * Cos(Zeta) + Zeta) / (Cos(Zeta)) ^ 2
        Zeta = Zeta - (f / fd) * damping
        
        'Label roots
        If j = 1 Then
            Label_z1.Caption = Format(Zeta, "0.0000")
        ElseIf j = 2 Then
            Label_z2.Caption = Format(Zeta, "0.0000")
        ElseIf j = 3 Then
            Label_z3.Caption = Format(Zeta, "0.0000")
        Else
            Label_z4.Caption = Format(Zeta, "0.0000")
        End If
        
   Loop While Abs(f) > tolerance
      
Next j
End Sub

Private Sub Command2_Click()
End
End Sub

Private Sub Label9_Click()

End Sub