22) \( \lim _{x \rightarrow 4} \frac{\sqrt{2 x+1}-3}{\sqrt{x-2}-\sqrt{2}}= \) 23) \( \lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+p^{2}}-p}{\sqrt{x^{2}+q^{2}}-q}= \)

To solve the first limit, we start by substituting \(x = 4\) in the expression \( \frac{\sqrt{2 x+1}-3}{\sqrt{x-2}-\sqrt{2}} \). This results in an indeterminate form \( \frac{0}{0} \). To resolve this, we can use algebraic manipulation. By multiplying the numerator and the denominator by the conjugates, we can simplify the expression and ultimately find that the limit evaluates to 2. For the second limit, we can set \(x = 0\) to obtain another indeterminate form \( \frac{0}{0} \). Here, we can apply L'Hôpital's Rule or further algebraic simplifications. Working it through step-by-step using differentiation or rationalizing the radicals will lead us to find that the limit evaluates to 1, provided \(p\) and \(q\) are positive constants.