Tentukan hasil dari:
[tex]\rm\displaystyle(a.)~~\lim _{x\to\infty}~~\frac{2x^4}{5x^5-x^2}\\\\(b.)~~\lim _{x\to\infty}~~\frac{4x^5+3x^4~.~.~.}{2x^3-5x^2~.~.~.}\\\\(c.)~~\lim _{x\to\infty}~~6x+3-\sqrt{36x^2+12x+4}\\\\(d.)~~\lim _{x\to\infty}~~\frac{x^5}{x^5}[/tex]
Penjelasan dengan langkah-langkah:
prinsip limit tak hingga = dibagi dengan pangkat terbesar
a. lim x-> tak hingga 2x^4 / 5x^5 - x²
= (2x^4 / x^5) / (5x^5 / x^5) - (x² / x^5)
= 0 / 5 - 0
= 0 / 5 = 0
b. lim x-> tak hingga (4x^5 + 3x^4) / (2x^3 - 5x²)
= ((4x^5 / x^5) + (3x^4 / x^5)) / ((2x^3 / x^5) - (5x² / x^5))
= 4 + 0 / 0 - 0
= 4 / 0
= tak hingga
c. lim x-> tak hingga 6x + 3 - √(36x² + 12x + 4)
= (6x + 3 - √(36x² + 12x + 4) x ((6x + 3) +√(36x² + 12x +4)) / ((6x + 3) +√(36x² + 12x +4))
= (36x² + 36x +9 - 36x² + 12x + 4) / (6x + 3) + √(36x² + 12x + 4)
= (48x + 13) / (6x + 3) + √(36x² + 12x + 4)
= 48 / 6 + √36
= 48 / 6 + 6
= 48 / 12
= 4
d. lim x-> tak hingga x^5 / x^5
= (x^5 / x^5) / (x^5 / x^5)
= 1 / 1
= 1
[answer.2.content]
