1.1-bo'lim : Ko'rib chiqish: Funktsiyalar
7. The farq koeffitsienti \(f\left( x \right)\) funksiyasi quyidagicha aniqlanadi:
\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\]\(f\left( t \right) = 2{t^2} - 3t + 9\) uchun farq koeffitsientini hisoblang.
Maslahat: Funktsiya endi \(f\left( t \right)\) ekanligidan hayajonlanmang, farq koeffitsienti hozirda \(x\) o'rniga \(t\) ga ega bo'lgan tarzda ishlaydi. Shunday qilib, \(f\left( {t + h} \right)\) ni hisoblang, so'ngra suratni hisoblang va nihoyat farq koeffitsientini hisoblang.
Yechim
\[\begin{align*}f\left( {t + h} \right) & = 2{\left( {t + h} \right)^2} - 3\left( {t + h} \right) + 9 \\ & = 2\left( {{t^2} + 2th + {h^2}} \right) - 3t - 3h + 9\\ & = 2{t^2} + 4th + 2{h^2} - 3t - 3h + 9\end{align*}\]
2-qadam
\[f\left( {t + h} \right) - f\left( t \right) = 2{t^2} + 4th + 2{h^2} - 3t - 3h + 9 - \left( {2{t^2} - 3t + 9} \right) = 4th + 2{h^2} - 3h\]
3-qadam
\[\frac{{f\left( {t + h} \right) - f\left( t \right)}}{h} = \frac{{4th + 2{h^2} - 3h}}{h} = 4t + 2h - 3\]