tentang limit nih guys
Matematika
Vinvon
Pertanyaan
tentang limit nih guys
1 Jawaban
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1. Jawaban whongaliem
[tex] \lim_{x \to \ \frac{ \pi }{2} } \frac{sin (x + \frac{ \pi }{2}) }{ \sqrt{ \frac{x}{2} } - \sqrt{ \frac{ \pi }{4} } } = \lim_{x \to \ \frac{ \pi }{2} } \frac{[sin (x + \frac{ \pi }{2} )( \sqrt{ \frac{x}{2} } + \sqrt{ \frac{ \pi }{4} }) }{ (\sqrt{ \frac{x}{2} } - \sqrt{ \frac{ \pi }{4} })( \sqrt{ \frac{x}{2} } + \sqrt{ \frac{ \pi }{4} } ) } [/tex]
[tex]= \lim_{x \to \ \frac{ \pi }{2} } \frac{[sin (x + \frac{ \pi }{2})][ \sqrt{ \frac{x}{2} }+ \sqrt{ \frac{ \pi }{4} }] }{ \frac{x}{2} - \frac{ \pi }{4} } [/tex]
[tex]= \lim_{x \to \ \frac{ \pi }{2} } \frac{[ sin (x - \frac{ \pi }{2})] [ \sqrt{ \frac{x}{2} } + \sqrt{ \frac{ \pi }{4} }] }{ \frac{1}{2} (x - \frac{ \pi }{2} )} [/tex]
[tex]= \lim_{x \to \ \frac{ \pi }{2} } \frac{2 .sin (x - \frac{ \pi }{2} )}{(x - \frac{ \pi }{2}) } . (\sqrt{ \frac{x}{2}} + \sqrt{ \frac{ \pi }{4} }) [/tex]
[tex]= 2 . 1 . (\sqrt{ \frac{ \frac{ \pi }{2} }{2} } + \sqrt{ \frac{ \pi }{4} } )[/tex]
[tex]= 2 . (\sqrt{ \frac{ \pi }{4} } + \sqrt{ \frac{ \pi }{4} } )[/tex]
[tex]= 2 . 2 \sqrt{ \frac{ \pi }{4} } [/tex]
[tex]= 4 . \frac{1}{2} \sqrt{x} [/tex]
= 2√π