Final answer to the problem
$-\frac{1}{4}$
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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
$\lim_{x\to\infty }\left(\left(\sqrt{4x^2-x+1}-2x\right)\frac{\sqrt{4x^2-x+1}+2x}{\sqrt{4x^2-x+1}+2x}\right)$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(\left(\sqrt{4x^2-x+1}-2x\right)\frac{\sqrt{4x^2-x+1}+2x}{\sqrt{4x^2-x+1}+2x}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (4x^2-x+1)^(1/2)-2x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. The power of a product is equal to the product of it's factors raised to the same power. Multiply -1 times 4.
Final answer to the problem
$-\frac{1}{4}$
Exact Numeric Answer
$-0.25$
