Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Factor the polynomial $x+8x^2$ by it's greatest common factor (GCF): $x$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(\sqrt{\frac{x\left(1+8x\right)}{2x^2-1}}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of ((x+8x^2)/(2x^2-1))^(1/2) as x approaches infinity. Factor the polynomial x+8x^2 by it's greatest common factor (GCF): x. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. If we directly evaluate the limit \lim_{x\to\infty }\left(\frac{x\left(1+8x\right)}{2x^2-1}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.
