Nilai dari lim x mendekati 1 Tan (x-1) sin (1 - akar x)/ x kuadrat -2x+ 1

Nilai dari lim x mendekati 1 Tan (x-1) sin (1 – akar x)/ x kuadrat -2x+ 1

Jawab:

Penjelasan dengan langkah-langkah:

limit trigonometri

soal

$sf lim_{xto 1}~ dfrac{tan(x-1). sin(1-sqrt x)}{x^2 -2x+1}$

$sf lim_{xto 1}~ dfrac{tan(x-1). sin(1-sqrt x)}{(x-1)(x-1)}$

$sf = lim_{xto 1}~ dfrac{tan(x-1)}{x-1}~lim_{xto 1}~dfrac{sin(1-sqrt x)}{(x-1)}$

$sf= (1)~lim_{xto 1}~dfrac{sin(1-sqrt x)}{-(1-x)}$

$sf= dfrac{sin(1-sqrt x)}{-(1-sqrt x)(1+ sqrt x)}$

$sf= ~lim_{xto 1}~dfrac{1}{-(1+ sqrt x)}$

$sf= ~lim_{xto 1}~dfrac{1}{(1+1)} = dfrac{1}{2}$