Exercise
$\lim_{x\to\infty\:}\left(\frac{1+x-3x^3}{1+x^2+3x^3}\right)$
Step-by-step Solution
Learn how to solve limits by direct substitution problems step by step online. Find the limit of (1+x-3x^3)/(1+x^23x^3) as x approaches infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction . Simplify the fraction by x.
Find the limit of (1+x-3x^3)/(1+x^23x^3) as x approaches infinity
Final answer to the exercise
$-1$