Temp - Clavius

Soal 19

$lim_{x \to\sim} \frac{3 x^{6} - 5 x^{2}}{(1 - 3 x^{3})^{2}}$

Jawab:

Yang perlu diperhatikan hanya suku dengan pangkat terbesar saja, sedangkan suku-suku lain dengan pangkat lebih kecil akan bernilai 0.

$\begin{aligned} lim_{x \to\sim} \frac{3 x^{6} - 5 x^{2}}{(1 - 3 x^{2})^{3}} \\ lim_{x \to\sim} \frac{3 x^{6}}{(- 3 x^{2})^{3}} \\ lim_{x \to\sim} \frac{3 x^{6}}{- 27 x^{6}} \\ lim_{x \to\sim} \frac{3 x^{6}}{- 27 x^{6}} \\ lim_{x \to\sim} \frac{3}{- 27} \\ - \frac{1}{9} \end{aligned}$

Soal 31

$lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$

Lihat jawaban

Jawab:

$\begin{aligned} lim_{x \to 2} \frac{x^{2} - 4}{x - 2} \\ lim_{x \to 2} \frac{(x + 2) (x - 2)}{x - 2} \\ lim_{x \to 2} \frac{(x + 2) (x - 2)}{(x - 2)} \\ lim_{x \to 2} (x + 2) \\ 2 + 2 \\ 4 \end{aligned}$

Soal 33

$lim_{x \to 4} \frac{x^{2} - 4 x}{x - 4}$

Lihat jawaban

Jawab:

$\begin{aligned} lim_{x \to 4} \frac{x^{2} - 4 x}{x - 4} \\ lim_{x \to 4} \frac{x (x - 4)}{x - 4} \\ lim_{x \to 4} \frac{x (x - 4)}{x - 4} \\ lim_{x \to 4} x \\ 4 \end{aligned}$

$lim_{x \to\sim} \frac{(2 x^{2} - 7)^{3} . (6 x^{2} + 2 x)}{(3 + 4 x^{3}) . (3 x^{5} + 7 x)} = \dots$

(A) $2$

(B) $4$

(D) $8$

(E) $10$

$lim_{x \to 2} \frac{3 x - 6}{x - 3} = \dots$

(A) $0$

(B) $1$

(D) $3$

(E) $4$

Jawab: D

$\begin{aligned} lim_{x \to 2} \frac{3 x - 6}{x - 2} \\ lim_{x \to 2} \frac{3 (x - 2)}{x - 2} \\ 3 \end{aligned}$