Question

(1 point)
evaluate
\\(\lim_{x\to - 2}(x - 2)^{6}(-5x^{2})\\)
answer:
use the space below to enter the letters corresponding to the limit laws that you used to find this limit:
limit laws
a. sum law
b. root law
c. quotient law
d. constant multiple law
e. product law
f. difference law
g. power law
answer:
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Explanation:

Step1: Apply product law

$\lim_{x
ightarrow - 2}(x - 2)^{6}(-5x^{2})=\lim_{x
ightarrow - 2}(x - 2)^{6}\cdot\lim_{x
ightarrow - 2}(-5x^{2})$

Step2: Apply power law for $(x - 2)^{6}$ and constant - multiple law for $-5x^{2}$

First, $\lim_{x
ightarrow - 2}(x - 2)^{6}=((-2)-2)^{6}=(-4)^{6}=4096$. Second, $\lim_{x
ightarrow - 2}(-5x^{2})=-5\lim_{x
ightarrow - 2}x^{2}=-5\times(-2)^{2}=-20$.

Step3: Calculate the product

$4096\times(-20)=-81920$

Answer:

-81920
E, D, G