Problem 30 - College Algebra and Calculus: An Applied Approach

Question

Find the limit. $$ \lim _{x \rightarrow 4} \sqrt[3]{x+4} $$

Step-by-Step Solution

Answer

So, the limit of the given function as x approaches 4 is '2'.

Step 1: Understand the Problem

The function given is \(\sqrt[3]{x+4}\), and we are asked to find the limit of this function as x approaches 4.

Step 2: Substitution

Substituting the value '4' in place of 'x', we obtain \(\sqrt[3]{4+4}\) which simplifies to \(\sqrt[3]{8}\).

Step 3: Solving the cube root

Now as we know, the cube root of 8 is '2' (since \(2^3 = 8\)), thus \(\sqrt[3]{8}\) becomes '2'.