Soalnya hari ini harus di kumpul
Jawab:
Penjelasan dengan langkah-langkah:
Penjelasan dengan langkah-langkah:
Nomor 2
[tex] = \lim \limits_{x \to0} \frac{ \sin(6x) }{12x} [/tex]
[tex] = \frac{6}{12} [/tex]
[tex] = \frac{1}{2} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \tan(10x) }{5x} [/tex]
[tex] = \frac{10}{5} [/tex]
[tex] = 2[/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{4x}{ \sin(3x) } [/tex]
[tex] = \frac{4}{3} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{7x}{ \tan(5x) } [/tex]
[tex] = \frac{7}{5} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ax}{ \sin(bx) } [/tex]
[tex] = \frac{a}{b} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \tan(px) }{qx} [/tex]
[tex] = \frac{p}{q} [/tex]
[tex] \: [/tex]
Nomor 3
[tex] = \lim \limits_{x \to0} \frac{ \sin(3x) }{ \sin(5x) } [/tex]
[tex] = \frac{3}{5} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{3 \tan(5x) }{ \sin(6x) } [/tex]
[tex] = \frac{3.5}{6} [/tex]
[tex] = \frac{5}{2} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \tan(2x) }{ \tan(4x) } [/tex]
[tex] = \frac{2}{4} [/tex]
[tex] = \frac{1}{2} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{2 \sin(14x) }{3 \tan(2x) } [/tex]
[tex] = \frac{2.14}{3.2} [/tex]
[tex] = \frac{14}{3} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \sin(6x) }{ \tan(4x) } [/tex]
[tex] = \frac{6}{4} [/tex]
[tex] = \frac{3}{2} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{5 \tan(6x) }{4 \sin(10x) } [/tex]
[tex] = \frac{5.6}{4.10} [/tex]
[tex] = \frac{3}{4} [/tex]
[tex] \: [/tex]
Nomor 4
[tex] = \lim \limits_{x \to0} \frac{ \sin {}^{2} (x) }{ {x}^{2} } [/tex]
[tex] = \lim \limits_{x \to0} {( \frac{ \sin(x) }{x} )}^{2} [/tex]
[tex] = {(\lim \limits_{x \to0} \frac{ \sin(x) }{x} )}^{2} [/tex]
[tex] = {1}^{2} [/tex]
[tex] = 1[/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \sin(2x) \tan(3x) }{16 {x}^{2} } [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \sin(2x) }{16x} \times \lim \limits_{x \to0} \frac{ \tan(3x) }{x} [/tex]
[tex] = \frac{2}{16} \times \frac{3}{1} [/tex]
[tex] = \frac{3}{8} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{9 {x}^{2} }{ \tan {}^{2} (x) } [/tex]
[tex] = \lim \limits_{x \to0} {( \frac{9x}{ \tan(x) } )}^{2} [/tex]
[tex] = {(\lim \limits_{x \to0} \frac{9x}{ \tan(x) } )}^{2} [/tex]
[tex] = {9}^{2} [/tex]
[tex] = 81[/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{5 \tan {}^{2} (2x) }{ {x}^{2} \sin(4x) } [/tex]
[tex] = \lim \limits_{x \to0} \frac{5 \tan(2x) }{x} \times \lim \limits_{x \to0} \frac{ \tan(2x) }{x} \times \lim \limits_{x \to0} \frac{\tan(2x)}{ \sin(4x) } [/tex]
[tex] = \frac{5.2}{1} \times \frac{2}{1} \times \frac{2}{4}[/tex]
[tex] = 10[/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{2 \sin {}^{2} (x) }{10 {x}^{2} } [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \sin {}^{2} (x) }{5x {}^{2} } [/tex]
[tex] = \frac{1}{5} \times \lim \limits_{x \to0} \frac{ \sin {}^{2} (x) }{ {x}^{2} } [/tex]
[tex] = \frac{1}{5} \times \lim \limits_{x \to0} {( \frac{ \sin(x) }{x} )}^{2} [/tex]
[tex] = \frac{1}{5} \times {(\lim \limits_{x \to0} \frac{ \sin(x) }{x} )}^{2} [/tex]
[tex] = \frac{1}{5} \times {1}^{2} [/tex]
[tex] = \frac{1}{5} [/tex]
[tex] \: [/tex]
[tex] = \lim \limits_{x \to0} \frac{6 \sin {}^{4} (3x) }{ {x}^{2} \tan {}^{2} (5x) } [/tex]
[tex] = \lim \limits_{x \to0} \frac{6 \sin(3x) }{x} \times \lim \limits_{x \to0} \frac{ \sin(3x) }{x} \times \lim \limits_{x \to0} \frac{ \sin(3x) }{ \tan(5x) } \times \lim \limits_{x \to0} \frac{ \sin(3x) }{ \tan(5x) } [/tex]
[tex] = \frac{6.3}{1} \times \frac{3}{1} \times \frac{3}{5} \times \frac{3}{5} [/tex]
[tex] = \frac{486}{25} [/tex]
[answer.2.content]
