Question

Limit question

Answer 1

\[\lim_{x \rightarrow \infty} \frac{ \sin ^{2}x }{ x^2 + 1 }\]

Answer 2

Evaluate the numerator and denominator separately

As x => inf, sin^2 x stays between 0 and 1

As x => inf, x^2+1 approaches infinity

So you have a number between 0 and 1, divided by infinity.

What's a small number divided by infinity equal to?

Answer 3

A graph can also be useful here https://www.google.com/search?q=sin%5Ex&oq=sin%5Ex&aqs=chrome..69i57j0l3.2818j0&sourceid=chrome&ie=UTF-8#q=(sin(x))%5E2%2F(x%5E2%2B1)&safe=off