Limit x mendekati nol untuk

$frac{ sin(7x) }{3x - tan(2x) }$
Minta bantuannya ya :D

Limit x mendekati nol untuk

Penyelesaian:

$displaystyle lim_{x to 0} frac{sin(7x)}{3x-tan(2x)}$

Subtitusikan langsung

$displaystyle begin{aligned} lim_{x to 0} frac{sin(7x)}{3x-tan(2x)} &= frac{sinbig(7(0)big)}{3(0)-tanbig(2(0)big)} \ &= frac{sin(0)}{0-tan(0)} \ &= frac{0}{0} end{aligned}$

Karena bentuknya $frac{0}{0}$ , gunakan Dalil L'Hopital

$displaystyle begin{aligned} lim_{x to 0} frac{sin(7x)}{3x-tan(2x)} &= lim_{x to 0} frac{frac{d}{dx}big(sin(7x)big)}{frac{d}{dx}big(3x-tan(2x)big)} \ &= lim_{x to 0} frac{7cos(7x)}{3-2sec^2(2x)} \ &= frac{7cosbig(7(0)big)}{3-2sec^2big(2(0)big)} \ &= frac{7cdot1}{3-2cdot1} \ &= 7end{aligned}$

Jawaban:

$displaystyle boxed{bold{7}}$