Question

find the limit.
lim (6 - y)^(4/3) as y→ - 2
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. lim (6 - y)^(4/3) as y→ - 2 = (simplify your answer. type an integer or a simplified fraction.)
b. the limit does not exist.

Explanation:

Step1: Substitute the value of y

We substitute \(y = - 2\) into the function \((6 - y)^{\frac{4}{3}}\). First, find the value of \(6 - y\) when \(y=-2\).
\(6-(-2)=6 + 2=8\).

Step2: Calculate the power - value

Now we need to find \(8^{\frac{4}{3}}\). We know that \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\). So \(8^{\frac{4}{3}}=\sqrt[3]{8^{4}}\). Since \(8 = 2^{3}\), then \(8^{4}=(2^{3})^{4}=2^{12}\), and \(\sqrt[3]{8^{4}}=\sqrt[3]{2^{12}} = 2^{4}=16\).

Answer:

A. \(\lim_{y
ightarrow - 2}(6 - y)^{\frac{4}{3}}=16\)