limx->2 x²-4/3-√x²+5=
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limx->2 x²-4/3-√x²+5=
1 Jawaban
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1. Jawaban whongaliem
[tex] \lim_{x \to \ 2} \frac{ x^{2} - 4}{3 - \sqrt{ x^{2} + 5}} = \lim_{x \to \ 2} \frac{( x^{2} - 4) (3 + \sqrt{ x^{2} + 5}) }{(3 - \sqrt{ x^{2} + 5}) (3 + \sqrt{ x^{2} + 5} ) } [/tex]
[tex]= \lim_{x \to \ 2} \frac{( x^{2} - 4) (3 + \sqrt{ x^{2} + 5} )}{9 - ( x^{2} + 5)} [/tex]
[tex]= \lim_{x \to \ 2} \frac{( x^{2} - 4) ( \sqrt{ x^{2} + 5} )}{9 - x^{2} - 5} [/tex]
[tex]= \lim_{x \to \ 2} \frac{- ( - x^{2} + 4)(3 + \sqrt{ x^{2} + 5}) }{- x^{2} + 4} [/tex]
[tex]= \lim_{x \to \ 2} - (3 + \sqrt{ x^{2} + 5} )[/tex]
[tex]= - (3 + \sqrt{ 2^{2} + 5} )[/tex]
[tex]= - (3 + \sqrt{9} )[/tex]
= - (3 + 3)
= - 6