Final answer to the problem
$\frac{1}{\sqrt{2}}$
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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
$\lim_{x\to0}\left(\frac{\sqrt{2+x^2}-\sqrt{2-x^2}}{x^2}\frac{\sqrt{2+x^2}+\sqrt{2-x^2}}{\sqrt{2+x^2}+\sqrt{2-x^2}}\right)$
Learn how to solve differential calculus problems step by step online.
$\lim_{x\to0}\left(\frac{\sqrt{2+x^2}-\sqrt{2-x^2}}{x^2}\frac{\sqrt{2+x^2}+\sqrt{2-x^2}}{\sqrt{2+x^2}+\sqrt{2-x^2}}\right)$
Learn how to solve differential calculus problems step by step online. Find the limit of ((2+x^2)^(1/2)-(2-x^2)^(1/2))/(x^2) as x approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. x+0=x, where x is any expression. Combining like terms x^2 and x^2.
Final answer to the problem
$\frac{1}{\sqrt{2}}$
