Question

SOAL ada di lampiran yya Kkakk ...
Mkasih sebelumnya ..
A. [tex]\frac{8}{7}[/tex]
B. [tex]\frac{7}{8}[/tex]
C. [tex]\frac{5}{6}[/tex]
D. [tex]\frac{3}{4}[/tex]
E. [tex]\frac{2}{9}[/tex]

GGasah terburu-buru GPP , yang penting Jangan NGasal , Dibutuhkan segera ....

Answer 1

Verified answer

Jawab:

[tex]\displaystyle \bold{(A)~~\frac{8}{ 7 }}[/tex]

Penjelasan dengan langkah-langkah:

[tex]\displaystyle \lim_{x\to2}\frac{x^{4}-3x^{3}+2x^{2} -4x+8 }{x^{4}-5x^{3}+13x^{2} -24x+20 }[/tex]

faktor x⁴ - 3x³ + 2x² - 4x + 8

= (x - 2)²(x² + x + 2)

faktor x⁴ - 5x³ + 13x² - 24x + 20

= (x - 2)²(x² - x + 5)

Maka:

[tex]\displaystyle \lim_{x\to2}\frac{x^{4}-3x^{3}+2x^{2} -4x+8 }{x^{4}-5x^{3}+13x^{2} -24x+20 }[/tex]

[tex]\displaystyle \lim_{x\to2}\frac{(x-2)^{2}(x^{2} +x+2) }{(x-2)^{2}(x^{2} -x+5) }[/tex]

[tex]\displaystyle \lim_{x\to2}\frac{\bcancel{(x-2)^{2}}(x^{2} +x+2) }{\bcancel{(x-2)^{2}}(x^{2} -x+5) }[/tex]

[tex]\displaystyle \lim_{x\to2}\frac{(x^{2} +x+2) }{(x^{2} -x+5) }[/tex]

[tex]\displaystyle \frac{2^{2} +2+2}{2^{2} -2+5}[/tex]

[tex]= \displaystyle \frac{4 + 4 }{ 4 + 3 }[/tex]

[tex]= \displaystyle \bold{\frac{8}{ 7 }~~~(A)}[/tex]