Answer:
B. The Limit is 1
Step-by-step explanation:
Use the sandwhich theorem. The limit at both end as x approaches 0 is equal to 1, therefore f(x) must be equal to 1 as well because it's sandwhich between the two intervals.
Solving the Limits of the Endpoint:
[tex]\lim_{n \to 0} \frac{x^2-x^4}{x^2}=\frac{0}{0}[/tex]
This is an in-determinant form so you must use L'Hopitals rule.
[tex]\lim_{n \to 0} \frac{x^2-x^4}{x^2} \rightarrow \lim_{n \to 0} \frac{2x-4x^3}{2x} \rightarrow \lim_{n \to 0} \frac{2-12x^2}{2} =1[/tex]
[tex]\lim_{n \to 0} {\frac{1}{4}x^3+1}=1[/tex]
