Lim h->0 ((x+h)^2 + (x+h) + 1 - (x^2 + x +1))/h = . . . .

Lim h->0 ((x+h)^2 + (x+h) + 1 – (x^2 + x +1))/h = . . . .

Jawaban Terkonfirmasi

$text{Hasil dari} : : lim limits_{h to 0} frac{ {(x + h)}^{2} + (x + h) + 1 - ( {x}^{2} + x + 1)}{h} : : text{adalah} : : boxed{2x + 1}$

Pembahasan

$text{Turunan fungsi f(x) dinotasikan dengan} : : f'(x) : : text{atau} : : frac{df(x)}{dx} \$

Definisi Turunan

$lim limits_{h to 0} frac{f(x + h) - f(x)}{h} \$

Diketahui :

$text{ Limit suatu fungsi aljabar } : : lim limits_{h to 0} frac{ {(x + h)}^{2} + (x + h) + 1 - ( {x}^{2} + x + 1)}{h} \ \$

Ditanya :

$text{Hasil dari } : : lim limits_{h to 0} frac{ {(x + h)}^{2} + (x + h) + 1 - ( {x}^{2} + x + 1)}{h} \$

Jawab :

$: : : : : lim limits_{h to 0} frac{ {(x + h)}^{2} + (x + h) + 1 - ( {x}^{2} + x + 1)}{h} \ \ = lim limits_{h to 0} frac{ ({x}^{2} + 2xh + {h}^{2}) + (x + h) + 1 - ( {x}^{2} + x + 1)}{h} \ \ = lim limits_{h to 0} frac{ ({h}^{2} + 2xh + h) + ( {x}^{2} + x + 1) - ( {x}^{2} + x + 1)}{h} \ \ = lim limits_{h to 0} frac{ ({h}^{2} + 2xh + h) }{h} \ \ = lim limits_{h to 0} : (h + 2x + 1) \ \ = 0 + 2x + 1 \ \ = boxed{2x + 1} \ \$