limit
bentuk 0/0
faktor
Penjelasan dengan langkah-langkah:
[tex]\sf 1) lim_{x\to 4}\ \dfrac{x^2 -16}{x-4}[/tex]
[tex]\sf = lim_{x\to 4}\ \dfrac{(x- 4)(x+4)}{x-4}[/tex]
[tex]\sf = lim_{x\to 4}\ (x+4) = 4 + 4= 8[/tex]
[tex]\sf 2) lim_{x\to 3}\ \dfrac{x^2 -7x+12}{x^2-4x + 3}[/tex]
[tex]\sf= lim_{x\to 3}\ \dfrac{(x- 3)(x - 4)}{(x -3)(x - 1)}[/tex]
[tex]\sf= lim_{x\to 3}\ \dfrac{(x - 4)}{(x - 1)}=\dfrac{(3-4)}{(3-1)} = -\dfrac{1}{2}[/tex]
[tex]\sf 3) lim_{x\to 2}\ \dfrac{x^2 -4}{x^2-x -2}[/tex]
[tex]\sf = lim_{x\to 2}\ \dfrac{(x-2)(x+2)}{(x-2)(x + 1)}[/tex]
[tex]\sf = lim_{x\to 2}\ \dfrac{(x+2)}{(x + 1)} = \dfrac{2+2}{2+1} = \dfrac{4}{3}[/tex]
[tex]\sf 4) lim_{x\to 2}\ \dfrac{3x^2+10x-8}{x^2+3x-4}[/tex]
[tex]\sf=lim_{x\to -4}\ \dfrac{(x+4)(3x-2)}{(x+4)(x-1)}[/tex]
[tex]\sf=lim_{x\to -4}\ \dfrac{(3x-2)}{(x-1)} =\dfrac{3(-4)-2}{-4-1} = \dfrac{14}{5}[/tex]
[tex]\sf5)\ lim_{x\to 3}\ \dfrac{(x^2-9)}{x - 3}[/tex]
[tex]\sf=lim_{x\to 3}\ \dfrac{(x -3)(x + 3)}{(x - 3)}[/tex]
[tex]\sf=lim_{x\to 3}\ (x + 3)= 3 + 3= 6[/tex]
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