Question

a) Lim x - 2 / x²-4
x→2

b) Lim x² - 64 / x - 8
x→ 8

c) Lim x² - 36 / x + 6
x→ -6

d) Lim x - 7 / x² - 49
x→7

AYUDAAAA

Answer 1

a)

$lim \frac{x-2}{x^{2}-4 }\\\\Factorizar (x^{2}-4) \\\\\\ Tener-en-cuenta: a^{2}-b^{2} = (a+b)(a-b)\\\\lim \frac{x-2}{(x-2)(x+2)}\\\\lim \frac{1}{x+2}\\ \\lim \frac{1}{2+2} = \frac{1}{4}$

Lim (x-2)/(x²-4) = 1/4

x→2

b)

$lim\frac{x^{2}-64 }{x-8}\\ \\Factorizar : (x^{2}-64) \\Aplicar : a^{2} -b^{2} = (a+b)(a-b)\\\\lim \frac{(x+8)(x-8)}{(x-8)}\\ \\lim (x+8) = (8+8) = 16$

Lim (x²-64)/(x - 8 ) = 16

x→ 8

c)

$lim\frac{x^{2}-36 }{x+6}\\\\Factorizar (x^{2} -36)\\Aplicar : a^{2} - b^{2} = (a+b)(a-b)\\\\lim\frac{(x+6)(x-6)}{(x+6)} \\\\lim (x-6) = (-6-6) = -12$

Lim (x²-36)/(x + 6 ) = -12

x→ -6

d)

$lim\frac{x-7}{x^{2}-49}\\ \\ Factorizar : (x^{2}-49) \\\\lim\frac{x-7}{(x-7)(x+7)} \\\\lim\frac{1}{(x+7)} = \frac{1}{7+7} = \frac{1}{14}$

Lim (x-7)/(x²-49)  = 1/14

x→7