pakee cara
[tex]\sf \: lim_{x\to0} \: \: \frac{2 - {cos}^{2} 3x}{ {cos}^{}2x + 1 } [/tex]
[tex] \sf\frac{2 - {cos}^{2}3(0) }{cos2(0)+ 1} [/tex]
[tex]\sf \frac{2 - {cos}^{2}(0) }{cos(0 )+ 1} [/tex]
[tex] \frac{ \: \: 2 - {1}^{2} }{1 + 1} = \frac{2 - (1 \times 1)}{2} [/tex]
[tex] \frac{2 - 1}{2} = \sf\blue{ \frac{1}{2} }[/tex]
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Zzz!!
[tex] \displaystyle\rm \: \lim_{ x \to0} \frac{2 - \cos ^{2} (3x) }{ \cos(2x) + 1 } [/tex]
[tex] \displaystyle\rm \: = \lim_{ x \to0} \frac{2 - (1 - \sin ^{2} (3x)) }{ 2 \sin^{2} (x) + 1 } [/tex]
[tex] \displaystyle\rm \: = \lim_{ x \to0} \frac{2 - 1 + \sin ^{2} (3x)}{ 2 \sin^{2} (x) + 1 } [/tex]
[tex] \displaystyle\rm \: = \lim_{ x \to0} \frac{1 + \sin ^{2} (3x)}{ 2 \sin^{2} (x) + 1 } [/tex]
[tex] \displaystyle\rm \: = \lim_{ x \to0} \frac{ \cancel{1 + \sin ^{2} (3x)}}{ 2 \: \cancel{\sin^{2} (x) + 1 }} [/tex]
[tex] \displaystyle\rm \: = \lim_{ x \to0} \frac{1}{2} [/tex]
[tex] \displaystyle\rm \: = \frac{1}{2} [/tex]
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