The statement second is correct because the end behavior is that as x = ±∞ , f(x) → 0
A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have a function:
[tex]\rm f(x) = \frac{7x^2+x+1}{x^4+1}[/tex]
Applying limit:
[tex]\lim_{x \to \pm \infty} \rm f(x)[/tex]
[tex]\rm \lim_{x \to \pm\infty} \frac{7x^2+x+1}{x^4+1}[/tex]
Divide by x^4 on the numerator and denominator, we get:
[tex]\rm \lim_{x \to \pm\infty} \frac{7/x^4+1/x^3+1/x^4}{1+1/x^4}[/tex]
So the value of the limit will be zero whereas x tends to ±∞
Thus, the statement second is correct because the end behavior is that as x = ±∞ , f(x) → 0
Learn more about the limit here:
brainly.com/question/8533149
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