lim (x→0) (tan²2x)/(xsin2xcos2x) = ... A. 1 B. 2 C. 3 D. 4 E. 5

<p><strong><u>Jawaban yang benar adalah B.</u></strong></p><p>&nbsp;</p><p><strong>Rumus:</strong></p><p>tan 2x = sin 2x/cos 2x</p><p>lim(x→0) sin px/sin qx= p/q</p><p>cos 0 = 1</p><p>cos ² 0 = (1)² = 1</p><p>&nbsp;</p><p>lim (x→0) (tan²2x)/(xsin2xcos2x)</p><p>= lim (x→0) (tan2x.tan 2x)/(<i>x.</i>sin2x.cos2x)</p><p>= lim (x→0) (tan2x/x).(tan 2x/sin2x.cos2x)</p><p>= lim (x→0) {2(tan 2x}/sin2x.cos2x)</p><p>= lim (x→0) {2(sin 2x/cos 2x}/sin2x.cos2x)</p><p>= lim (x→0) {2(sin 2x/cos 2x)}/sin2x.cos2x)</p><p>= lim (x→0) (2(<i><strong>sin 2x</strong></i>/cos 2x) <strong>× </strong>(1/<i><strong>sin2x</strong></i>.cos2x) (sin2x dicoret karena sudah sama)</p><p>= lim (x→0) (2/cos² 2x)</p><p>substitusi x = 0:</p><p>= (2/cos² 2(0))</p><p>= 2/cos² 0</p><p>= 2/1</p><p>= 2</p><p>&nbsp;</p><p>Dengan demikian, lim (x→0) (tan²2x)/(xsin2xcos2x) adalah 2.</p>