Pertanyaan

Untuk soal nomor 7- 13, tentukan harga-hanga limitnya dengan terlebih dahulu mengalikannya dengan bentuk sekawan.

Hitunglah limit fungsi berikut! h → 0 lim h x + h − x

Hitunglah limit fungsi berikut!

$h \to 0 lim \frac{x + h - x}{h}$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $size 14px lim with size 14px h size 14px rightwards arrow size 14px 0 below fraction numerator square root of size 14px x size 14px plus size 14px h end root size 14px minus square root of size 14px x over denominator size 14px h end fraction$ adalah $fraction numerator 1 over denominator 2 x end fraction square root of x$ .

Pembahasan

Pertama, disubtitusikan pada limit tersebut Karena menghasilkan limit bentuk tak tentumaka akan ditentukan dengan mengalikanakar sekawan Jadi, nilai adalah .

Pertama, disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as h rightwards arrow 0 of fraction numerator square root of x plus h end root minus square root of x over denominator h end fraction equals fraction numerator square root of x plus 0 end root minus square root of x over denominator 0 end fraction equals 0 over 0 end style$

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan mengalikan akar sekawan

$space space space space space limit as h rightwards arrow 0 of fraction numerator square root of x plus h end root minus square root of x over denominator h end fraction times fraction numerator square root of x plus h end root plus square root of x over denominator square root of x plus h end root plus square root of x end fraction left right double arrow limit as h rightwards arrow 0 of fraction numerator open parentheses x plus h close parentheses minus x over denominator h open parentheses square root of x plus h end root minus square root of x close parentheses end fraction left right double arrow limit as h rightwards arrow 0 of fraction numerator h over denominator h open parentheses square root of x plus h end root minus square root of x close parentheses end fraction left right double arrow fraction numerator 1 over denominator open parentheses square root of x plus 0 end root minus square root of x close parentheses end fraction left right double arrow fraction numerator 1 over denominator 2 square root of x end fraction equals fraction numerator 1 over denominator 2 x end fraction square root of x$

Jadi, nilai $size 14px lim with size 14px h size 14px rightwards arrow size 14px 0 below fraction numerator square root of size 14px x size 14px plus size 14px h end root size 14px minus square root of size 14px x over denominator size 14px h end fraction$ adalah $fraction numerator 1 over denominator 2 x end fraction square root of x$ .