Question

Soal Mat Kelas 11 Dengan Cara​

Answer 1

Penjelasan dengan langkah-langkah:

semoga menjadi jawaban terbaik

Answer 2

Nomor 6

a

pasangan sekawan

[tex] = 5 - \sqrt{2 x + 1} \times \frac{5 + \sqrt{2x + 1} }{5 + \sqrt{2x + 1} } [/tex]

hasil kali

[tex] = 5 - \sqrt{2 x + 1} \times \frac{5 + \sqrt{2x + 1} }{5 + \sqrt{2x + 1} } [/tex]

[tex] = \frac{25 - (2x + 1)}{5 + \sqrt{2x + 1} } [/tex]

[tex] = \frac{ - 2x + 24}{5 + \sqrt{2x + 1} } [/tex]

b

pasangan sekawan

[tex] = \sqrt{x - 1} - 3 \times \frac{ \sqrt{x - 1} + 3}{ \sqrt{x - 1} + 3} [/tex]

hasil kali

[tex] = \sqrt{x - 1} - 3 \times \frac{ \sqrt{x - 1} + 3}{ \sqrt{x - 1} + 3} [/tex]

[tex] = \frac{(x - 1) - 9}{ \sqrt{x - 1} + 3 } [/tex]

[tex] = \frac{x - 10}{ \sqrt{x - 1} + 3 } [/tex]

Nomor 7

[tex] = \lim_{x \to10} \: \frac{x - 10}{ \sqrt{x - 1} - 3 } [/tex]

[tex] = \lim_{x \to10} \: \frac{x - 10}{ \sqrt{x - 1} - 3 } \times \frac{ \sqrt{x - 1} + 3}{ \sqrt{x - 1} + 3} [/tex]

[tex]= \lim_{x \to10} \frac{(x - 10)( \sqrt{x - 1} + 3)}{(x - 1) - 9} [/tex]

[tex]= \lim_{x \to10} \frac{ \cancel{(x - 10)}( \sqrt{x - 1 } + 3) }{ \cancel{x - 10}} [/tex]

[tex] = \sqrt{(10) - 1} + 3[/tex]

[tex] = \sqrt{9} + 3[/tex]

[tex] = 3 + 3[/tex]

[tex] = 6[/tex]

Nomor 8

[tex]= \lim_{x \to12} \: \frac{5 - \sqrt{2x + 1} }{12 - x} [/tex]

[tex]= \lim_{x \to12} \: \frac{5 - \sqrt{2x + 1} }{12 - x} \times \frac{5 + \sqrt{2x + 1} }{5 + \sqrt{2x + 1} } [/tex]

[tex]= \lim_{x \to12} \: \frac{25 - (2x + 1)}{(12 - x)(5 + \sqrt{2x + 1}) } [/tex]

[tex] = \lim_{x \to12} \frac{ - 2x + 24}{(12 - x)(5 + \sqrt{2x + 1} )} [/tex]

[tex] = \lim_{x \to12} \frac{2 \cancel{(12 - x)}}{ \cancel{(12 - x)}(5 + \sqrt{2x + 1}) } [/tex]

[tex] = \frac{2}{5 + \sqrt{2(12) + 1} } [/tex]

[tex] = \frac{2}{5 + \sqrt{24 + 1} } [/tex]

[tex] = \frac{2}{5 + \sqrt{25} } [/tex]

[tex] = \frac{2}{5 + 5} [/tex]

[tex] = \frac{2}{10} [/tex]

[tex] = \frac{1}{5} [/tex]

Nomor 9

[tex]= \lim_{x \to \infty } \: \sqrt{7 {x}^{2} + 2x - 4} - \sqrt{7 {x}^{2} + 5x - 2} \\ [/tex]

[tex] = \frac{2 -5 }{2 \sqrt{7} } [/tex]

[tex] = \frac{ - 3}{2 \sqrt{7} } [/tex]

[tex] = \frac{ - 3}{2 \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } [/tex]

[tex] = \frac{ - 3 \sqrt{7} }{2(7)} [/tex]

[tex] = - \frac{3}{14} \sqrt{7} [/tex]