The relative error function of [tex]g(h,t) = \frac{2\cdot h}{t^{2}}[/tex] as a function of terms h, Δh, t, Δt is described by the rational expression [tex]\delta = \frac{t^{2}\cdot (h+\Delta h)}{h\cdot (t+\Delta t)^{2}}-1[/tex].
Relative error represents the measure of a unit deviation of a real value respect to an expected value, it represents an expression independent of magnitudes of values.
In this question we must apply the concept of relative error ([tex]\delta[/tex]real value ([tex]g(h+\Delta h, t + \Delta t)[/tex]theoretical value is divided by theoretical value ([tex]g(h, t)[/tex]relative error is characterized by this formula:
[tex]\delta = \frac{g(h+\Delta h, t+\Delta t)-g(h,t)}{g(h,t)}[/tex]
[tex]\delta = \frac{g(h+\Delta h, t+\Delta t)}{g(h, t)} -1[/tex] (1)
If we know that [tex]g(h,t) = \frac{2\cdot h}{t^{2}}[/tex], then the relative error formula is:
[tex]\delta = \frac{t^{2}\cdot (h+\Delta h)}{h\cdot (t+\Delta t)^{2}}-1[/tex]
The relative error function of [tex]g(h,t) = \frac{2\cdot h}{t^{2}}[/tex] as a function of terms h, Δh, t, Δt is described by the rational expression [tex]\delta = \frac{t^{2}\cdot (h+\Delta h)}{h\cdot (t+\Delta t)^{2}}-1[/tex]. [tex]\blacksquare[/tex]
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