Final answer to the problem
$-\frac{9}{2}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
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1
Applying rationalisation
$\lim_{x\to\infty }\left(\left(\sqrt{x^2-9x+1}-x\right)\frac{\sqrt{x^2-9x+1}+x}{\sqrt{x^2-9x+1}+x}\right)$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(\left(\sqrt{x^2-9x+1}-x\right)\frac{\sqrt{x^2-9x+1}+x}{\sqrt{x^2-9x+1}+x}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2-9x+1)^(1/2)-x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Cancel like terms x^2 and -x^2. 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 .
Final answer to the problem
$-\frac{9}{2}$
Exact Numeric Answer
$-4.5$
