Evaluate the following limits, show all your work with good form and indicate which algebraic tools you used. (substitution, factoring, rationalizing, change of variable) 1. $\lim _{x_{-} \rightarrow 3} \frac{x^{3}-21}{2 x+3}$ 2. $\lim _{x_{-} \rightarrow 3} \frac{9-x^{2}}{3-x}$ 3. $\lim _{x_{-} \rightarrow 0} \frac{\sqrt{1+4 x}-\sqrt{1+x}}{x}$ 4. $\lim _{h \rightarrow 0} \frac{(1+h)^{\frac{1}{6}}-1}{h}$

Step 1 ：The first question is asking for the limit of the function \(\frac{x^{3}-21}{2 x+3}\) as \(x\) approaches \(3\) from the left.

Step 2 ：To solve this, we can simply substitute \(x=3\) into the function and evaluate it.

Step 3 ：This is because the function is continuous at \(x=3\), and the limit from the left is equal to the function value at that point.

Step 4 ：Substituting \(x=3\) into the function, we get \(\frac{3^{3}-21}{2 \cdot 3+3} = \frac{2}{3}\).

Step 5 ：Final Answer: The limit of the function \(\frac{x^{3}-21}{2 x+3}\) as \(x\) approaches \(3\) from the left is \(\boxed{\frac{2}{3}}\).