Matematika Sekolah Menengah Atas limit fungsi kelas XI ​

limit fungsi kelas XI ​

Jawab:

limit x-> a
subsitusi langsung

faktorisasi

a.  lim x->  -2  -x² + 3x + 2
x= - 2 ,  limit =  -( -2)² + 3(-2) + 2
limit = - 4 - 6 + 2
limit = - 8

b)

[tex]\sf lim_{x\to 3}~ \dfrac{x^3 - 27}{2x^2- 5x - 3}[/tex]

faktorisasikan

[tex]\sf lim_{x\to 3}~ \dfrac{( x- 3)(x^2 + 3x +9)}{(x-3)(2x + 1)}[/tex]

[tex]\sf lim_{x\to 3}~ \dfrac{(x^2 + 3x +9)}{(2x + 1)}[/tex]

[tex]\sf lim_{x\to 3}~ \dfrac{3^2 + 3(3) +9}{2(3) + 1} = \dfrac{27}{7}[/tex]

c.

[tex]\sf lim_{x\to 0}~ \dfrac{x^2-5x}{x^3+2x^2 - 3x}[/tex]

[tex]\sf lim_{x\to 0}~ \dfrac{x(x - 5)}{x(x^2 +2x - 3)}[/tex]

[tex]\sf lim_{x\to 0}~ \dfrac{x - 5}{x^2 +2x - 3}[/tex]

x= 0,

[tex]\sf lim_{x\to 0}~ \dfrac{- 5}{- 3} = \dfrac{5}{3}[/tex]

d.

[tex]\sf lim_{x\to 4}~ \dfrac{\sqrt{3x+4}-(3x-8)}{x^2 -16}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{3x+4-(3x-8)^2}{(x^2 -16)(4+4)}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{3x+4-(9x^2 - 48x + 64)}{(x^2 -16)(4+4)}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{3x+4-9x^2 + 48x - 64}{(x^2 -16)(8)}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{-9x^2 + 51x - 60}{(x-4)(x + 4)(8)}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{(x- 4)(-9x + 15)}{(x-4)(x + 4)(8)}[/tex]

[tex]\sf lim_{x\to 4}~ \dfrac{-9x + 15}{(x + 4)(8)}[/tex]

x= 4

[tex]\sf lim_{x\to 4}~ \dfrac{-9(4) + 15}{(4 + 4)(8)} = - \dfrac{21}{64}[/tex]

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