Find the limit of $\sqrt{3+x}-\sqrt{3}$ as $x$ approaches 0

Step-by-step Solution

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Final answer to the problem

0

Step-by-step Solution

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  • Solve using L'Hôpital's rule
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  • Solve the limit using factorization
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  • Integrate by partial fractions
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Evaluate the limit $\lim_{x\to0}\left(\sqrt{3+x}-\sqrt{3}\right)$ by replacing all occurrences of $x$ by $0$

$\sqrt{3+0}-\sqrt{3}$

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$\sqrt{3+0}-\sqrt{3}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (3+x)^(1/2)-3^(1/2) as x approaches 0. Evaluate the limit \lim_{x\to0}\left(\sqrt{3+x}-\sqrt{3}\right) by replacing all occurrences of x by 0. Add the values 3 and 0. Cancel like terms \sqrt{3} and -\sqrt{3}.

Final answer to the problem

0

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Function Plot

Plotting: $\sqrt{3+x}-\sqrt{3}$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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