Limit x tak hingga
trigonometri
Penjelasan dengan langkah-langkah:
tentukan hasil limit
[tex]\sf 7). \lim_{x\to \infty} \ \dfrac{4}{x^2\sin \frac{2}{x}.\tan \frac{6}{x}}[/tex]
[tex]\sf misal \ a= \frac{1}{x} , x= \infty , maka \ a = 0[/tex]
[tex]\sf \lim_{a\to 0} \ \dfrac{4}{(\frac{1}{a})^2\sin 2a.\tan 6a}[/tex]
[tex]\sf \lim_{a\to 0} \ \dfrac{4a^2}{\sin 2a.\tan 6a} = \dfrac{4}{2(6)} = \frac{1}{3}[/tex]
[tex]\sf 8). \lim_{x\to \infty} \ \dfrac{\frac{5}{x^2}\tan\ \frac{3}{x}}{\sin \frac{6}{x}.\tan^2 \frac{4}{x}}[/tex]
[tex]\sf misal \ a= \frac{1}{x} , x= \infty , maka \ a = 0[/tex]
[tex]\sf \lim_{a\to 0} \ \dfrac{5a^2\tan\ 3a}{\sin 6a.\tan^2 4a}[/tex]
[tex]\sf \lim_{a\to 0} \ \dfrac{5a^2(3a)}{6a.(4a)^2}[/tex]
[tex]\sf \lim_{a\to 0} \ \dfrac{15a^3}{96a^3} =\dfrac{15}{96}=\dfrac{5}{32}[/tex]
