Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim x→8 3 + 3x1 − 5x2 + x3
Question
Evaluate the limit using the appropriate Limit Law(s).
(If an answer does not exist, enter DNE.)
\lim_{x \to 8} \frac{3 + 3x}{1 - 5x^2 + x^3}
Solution
To evaluate the limit of the function as x approaches 8, we can simply substitute 8 into the function because it is a polynomial function and polynomial functions are continuous everywhere.
The function is: f(x) = 3 + 3x/(1 - 5x + x^3)
Substitute x = 8 into the function:
f(8) = 3 + 38/(1 - 58 + 8^3)
= 3 + 24/(1 - 40 + 512)
= 3 + 24/473
= 3 + 0.05074
= 3.05074
So, the limit of the function as x approaches 8 is 3.05074.
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