Nilai dari lim x tak hingga x cot 1 /x sin 1/x kuadrat

<p>Jawaban : 1</p><p>&nbsp;</p><p>Ingat kembali:</p><p>Lim x→0 [(sin ax)/(tan bx)] = a/b</p><p>&nbsp;</p><p>Diketahui:</p><p>Lim x→∞ [cot (1/x) . sin 1/x]</p><p>&nbsp;</p><p>Misalkan :</p><p>1/x = y → x = 1/y</p><p>&nbsp;</p><p>Maka:</p><p>Lim x→∞ [cot (1/x) . sin 1/x]</p><p>= Lim y→0 [cot y . sin y]</p><p>= Lim y→0 [1/(tan y) . sin y]</p><p>= Lim y→0 [(sin y)/(tan y)]</p><p>= 1</p><p>&nbsp;</p><p>Jadi, Lim x→∞ [cot (1/x) . sin 1/x] = 1.</p>