started: oct 20 at 9:55pm\nquiz instructions\naccess code: start\ntimed: 25 minutes\nnumber of attempts…

started: oct 20 at 9:55pm\nquiz instructions\naccess code: start\ntimed: 25 minutes\nnumber of attempts: 1\nlockdown browser and respondus monitor required.\nthis quiz covers sections through 3.7 from the textbook.\nquestion 2\nfind the limit, if it exists:\n$$\\lim_{x \\to \\infty} \\frac{x^{5}}{\\sqrt{x^{10}+5}}$$\n1\ndne\n1/2\n5\n0

started: oct 20 at 9:55pm\nquiz instructions\naccess code: start\ntimed: 25 minutes\nnumber of attempts: 1\nlockdown browser and respondus monitor required.\nthis quiz covers sections through 3.7 from the textbook.\nquestion 2\nfind the limit, if it exists:\n$$\\lim_{x \\to \\infty} \\frac{x^{5}}{\\sqrt{x^{10}+5}}$$\n1\ndne\n1/2\n5\n0

Answer

Explanation:

Step1: Simplify the denominator

When (x\to\infty), (\sqrt{x^{10}+5}=\sqrt{x^{10}(1 + \frac{5}{x^{10}})}=x^{5}\sqrt{1+\frac{5}{x^{10}}}) (since (x>0) as (x\to\infty)).

Step2: Substitute into the original limit

The original limit (\lim_{x\to\infty}\frac{x^{5}}{\sqrt{x^{10}+5}}=\lim_{x\to\infty}\frac{x^{5}}{x^{5}\sqrt{1+\frac{5}{x^{10}}}}).

Step3: Cancel out (x^{5})

Cancel (x^{5}) (for (x\neq0)), we get (\lim_{x\to\infty}\frac{1}{\sqrt{1+\frac{5}{x^{10}}}}).

Step4: Evaluate the limit

As (x\to\infty), (\frac{5}{x^{10}}\to0). So (\lim_{x\to\infty}\frac{1}{\sqrt{1+\frac{5}{x^{10}}}}=\frac{1}{\sqrt{1 + 0}}=1).

Answer:

A. 1