Respuesta :
The given vector Field f(x,y)= [tex]3x^{2} - 5y^{2}[/tex] is not Conservative.
What is Conservative Vector Field?
A conservative vector field is a vector field that is the gradient of some function.
The integral is independent of the path that C takes going from its starting point to its ending point.
We know that , the function F conservative if
[tex]\frac{ dP}{dy}[/tex] = [tex]\frac{dQ}{dx}[/tex]
If we prove opposite of this then the function F is not conservative
We have given function , f(x,y)= [tex]3x^{2} - 5y^{2}[/tex]
let P(x,y) = [tex]3x^{2} - 5y^{2}[/tex] and Q (x,y) =0
Now, [tex]\frac{dP}{dy}[/tex] = -10y
and, [tex]\frac{dQ}{dx}[/tex] = 0
Since [tex]\frac{dP}{dy}[/tex] ≠ [tex]\frac{dQ}{dx}[/tex]
Hence, the field is not conservative.
Learn more about Conservative vector here: brainly.com/question/15236009
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