The formula for resonant frequency is:
[tex]f_0=\frac{1}{2\pi\sqrt{LC} }[/tex]
Given information:
[tex]f_{0\text{,small}}=500 \text{ kHz}\\f_{0\text{,large}}=1650 \text{ kHz}\\L=3.83\text{ } \mu \text{H}[/tex]
Plug in the given values to find one value of capacitance:
[tex]500 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.645*10^{-8} \text{ F}=26.45 \text{ nF}[/tex]
Plug in the given values to find the other value of capacitance:
[tex]1650 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.429*10^{-8} \text{ F}=2.429 \text{ nF}[/tex]
This gives a range of 2.429 nF to 26.45 nF.
With significant figures taken into account, the range of capacitance is 2.43 nF to 30 nF.
