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Find the limit of $\sqrt{4x^2+35}-2x$ as $x$ approaches $\infty $

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Solution

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Final answer to the problem

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Step-by-step Solution

How should I solve this problem?

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  • 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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Applying rationalisation

Learn how to solve limits by rationalizing problems step by step online.

$\lim_{x\to\infty }\left(\left(\sqrt{4x^2+35}-2x\right)\frac{\sqrt{4x^2+35}+2x}{\sqrt{4x^2+35}+2x}\right)$

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of (4x^2+35)^(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

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Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $\sqrt{4x^2+35}-2x$

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Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

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