no 2,5,6, sm caranya
Matematika
zvkif
Pertanyaan
no 2,5,6, sm caranya
2 Jawaban
-
1. Jawaban arsetpopeye
2) Lim (x^2 - √x)/(1 - x^2)
= (3^2 - √3)/(1 - 3^2)
= (9 - √3)/(1 - 9)
= (9 - √3)/(-8)
= (√3 - 9)/8
= 1/8 (√3 - 9)
5) Lim (4 - x^2)/(3 - √(x^2 + 5))
= Lim (4 - x^2)/(3 - √(x^2 + 5)) . (3 + √(x^2 + 5))/(3 + √(x^2 + 5))
= Lim (4 - x^2)(3 + √(x^2 + 5)) / (9 - (x^2 + 5))
= Lim (4 - x^2)(3 + √(x^2 + 5)) / (4 - x^2)
= Lim (3 + √(x^2 + 5))
= 3 + √(2^2 + 5)
= 3 + √(4 + 5)
= 3 + √9
= 6
6) Lim (x - 3)/(√x - √3)
= Lim (√x + √3)(√x - √3)/(√x - √3)
= Lim (√x + √3)
= √3 + √3
= 2√3 -
2. Jawaban whongaliem
[tex]2) \lim_{x \to \ 3} \frac{ x^{2} - \sqrt{x} }{1 - x^{2} } = \frac{ 3^{2} - \sqrt{3} }{1 - x^{2} } [/tex]
[tex]= \frac{9 - \sqrt{3} }{1 - 9} [/tex]
[tex]= - \frac{1}{8} (9 - \sqrt{3} )[/tex]
[tex]5) \lim_{x \to \ 2} \frac{4 - x^{2} }{3 - \sqrt{ x^{2} + 5}} = \lim_{x \to \ 2} \frac{(4 - x^{2} )( 3 + \sqrt{ x^{2} + 5} }{(3 - \sqrt{ x^{2} + 5}) (3 + \sqrt{ x^{2} + 5}) } [/tex]
[tex]= \lim_{x \to \ 2} \frac{(4 - x^{2} )( 3 + \sqrt{ x^{2} + 5}) }{9 - ( x^{2} + 5)} [/tex]
[tex] \lim_{x\to \ 2} \frac{(4 - x^{2} )(3 + \sqrt{ x^{2} + 5}) }{9 - x^{2} - 5} [/tex]
[tex]= \lim_{x \to \ 2} \frac{(4 - x^{2} )(3 + \sqrt{ x^{2} + 5} )}{4 - x^{2} } [/tex]
[tex]= \lim_{x \to \ 2} 3 + \sqrt{ x^{2} + 5} [/tex]
[tex]= 3 + \sqrt{ 2^{2} + 5} [/tex]
[tex]= 3 + \sqrt{4 + 5} [/tex]
= 3 + √9
= 3 + 3
= 6
[tex]6) \lim_{x \to \ -3} \frac{x - 3}{ \sqrt{x} - \sqrt{3} } = \lim_{x\to \ - 3} \frac{( \sqrt{x} + \sqrt{3} ) ( \sqrt{x} - \sqrt{3}) }{ \sqrt{x} - \sqrt{3} } [/tex]
[tex]= \lim_{x \to \ - 3} \sqrt{x} + \sqrt{3} [/tex]
= √-3 + √3
= i√3 + √3