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Exercise

$\lim_{x\to0}\left(\frac{\sqrt{8+x}-2\sqrt{2}}{x}\right)$

Step-by-step Solution

Learn how to solve limits by rationalizing problems step by step online. Find the limit of ((8+x)^(1/2)-2*2^(1/2))/x as x approaches 0. 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 8.
Find the limit of ((8+x)^(1/2)-2*2^(1/2))/x as x approaches 0

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Final answer to the exercise

$\frac{1}{\sqrt{8}+\sqrt{\left(2\right)^{3}}}$

Try other ways to solve this exercise

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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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Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

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