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

$sf lim_{xto 3}~ dfrac{x^3 - 27}{2x^2- 5x - 3}$

faktorisasikan

$sf lim_{xto 3}~ dfrac{( x- 3)(x^2 + 3x +9)}{(x-3)(2x + 1)}$

$sf lim_{xto 3}~ dfrac{(x^2 + 3x +9)}{(2x + 1)}$

$sf lim_{xto 3}~ dfrac{3^2 + 3(3) +9}{2(3) + 1} = dfrac{27}{7}$

$sf lim_{xto 0}~ dfrac{x^2-5x}{x^3+2x^2 - 3x}$

$sf lim_{xto 0}~ dfrac{x(x - 5)}{x(x^2 +2x - 3)}$

$sf lim_{xto 0}~ dfrac{x - 5}{x^2 +2x - 3}$

x= 0,

$sf lim_{xto 0}~ dfrac{- 5}{- 3} = dfrac{5}{3}$

$sf lim_{xto 4}~ dfrac{sqrt{3x+4}-(3x-8)}{x^2 -16}$

$sf lim_{xto 4}~ dfrac{3x+4-(3x-8)^2}{(x^2 -16)(4+4)}$

$sf lim_{xto 4}~ dfrac{3x+4-(9x^2 - 48x + 64)}{(x^2 -16)(4+4)}$

$sf lim_{xto 4}~ dfrac{3x+4-9x^2 + 48x - 64}{(x^2 -16)(8)}$

$sf lim_{xto 4}~ dfrac{-9x^2 + 51x - 60}{(x-4)(x + 4)(8)}$

$sf lim_{xto 4}~ dfrac{(x- 4)(-9x + 15)}{(x-4)(x + 4)(8)}$

$sf lim_{xto 4}~ dfrac{-9x + 15}{(x + 4)(8)}$

x= 4

$sf lim_{xto 4}~ dfrac{-9(4) + 15}{(4 + 4)(8)} = - dfrac{21}{64}$