find the limit.\n\n$$\\lim_{y \\to -3}(5 - y)^{\\frac{2}{3}}$$\n\nselect the correct choice below and, if…

find the limit.\n\n$$\\lim_{y \\to -3}(5 - y)^{\\frac{2}{3}}$$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. $$\\lim_{y \\to -3}(5 - y)^{\\frac{2}{3}} = $$ (simplify your answer. type an integer or a simplified fraction.)\n\nb. the limit does not exist.

find the limit.\n\n$$\\lim_{y \\to -3}(5 - y)^{\\frac{2}{3}}$$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. $$\\lim_{y \\to -3}(5 - y)^{\\frac{2}{3}} = $$ (simplify your answer. type an integer or a simplified fraction.)\n\nb. the limit does not exist.

Answer

Explanation:

Step1: Substitute (y = - 3) into the function

Substitute (y=-3) into ((5 - y)^{\frac{2}{3}}). We get (5-(-3)=5 + 3=8). So the function becomes (8^{\frac{2}{3}}).

Step2: Simplify the exponent

We know that (a^{\frac{m}{n}}=\sqrt[n]{a^{m}}). For (8^{\frac{2}{3}}), we can write it as (\sqrt[3]{8^{2}}) or ((\sqrt[3]{8})^{2}). Since (\sqrt[3]{8}=2) (because (2\times2\times2 = 8)), then ((\sqrt[3]{8})^{2}=2^{2}).

Answer:

A. (\lim_{y\rightarrow - 3}(5 - y)^{\frac{2}{3}}=4)