Nilai lim x 1sin²(x-1)/x²-2x+1

Kalkulus Matematika · SMA easy

Nilai $\displaystyle\lim_{x\to1}\dfrac{\sin^2(x-1)}{x^2-2x+1}=....$

Kunci jawaban

$x^2-2x+1=(x-1)^2$ , sehingga bentuknya $\left(\dfrac{\sin(x-1)}{x-1}\right)^2\to1$ .

Penyebut $x^2-2x+1=(x-1)^2$ . Misal $u=x-1\to0$ :

$\dfrac{\sin^2 u}{u^2}=\left(\dfrac{\sin u}{u}\right)^2\to1^2=1$ .

Jawabannya B.