Questions: lim as x approaches 4 of the cube root of (x+4)

lim as x approaches 4 of the cube root of (x+4)
Transcript text: \(\lim _{x \rightarrow 4} \sqrt[3]{x+4}\)
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Solution

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Solution Steps

To find the limit of the function as \( x \) approaches 4, we can directly substitute \( x = 4 \) into the function since it is continuous at that point.

Step 1: Define the Function

We are given the function \( f(x) = \sqrt[3]{x + 4} \).

Step 2: Evaluate the Limit

To find the limit as \( x \) approaches 4, we substitute \( x = 4 \) into the function: \[ \lim_{x \to 4} \sqrt[3]{x + 4} = \sqrt[3]{4 + 4} = \sqrt[3]{8} \]

Step 3: Simplify the Expression

Simplify the expression: \[ \sqrt[3]{8} = 2 \]

Final Answer

\(\boxed{2}\)

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