Final answer to the problem
$-2$
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Step-by-step Solution
How should I solve this problem?
- Solve without using l'Hôpital
- Solve using L'Hôpital's rule
- 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
- Integrate by substitution
- Load more...
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1
Applying rationalisation
$\lim_{x\to0}\left(\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}\frac{\sqrt{1-x}+\sqrt{1+3x}}{\sqrt{1-x}+\sqrt{1+3x}}\right)$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to0}\left(\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}\frac{\sqrt{1-x}+\sqrt{1+3x}}{\sqrt{1-x}+\sqrt{1+3x}}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of ((1-x)^(1/2)-(1+3x)^(1/2))/x 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 and -3x.
Final answer to the problem
$-2$
