\( \frac{d}{dx}(y^{3}\sqrt {x^{2}+y})=\frac{d}{dx}(x) \)

Show that \( \Gamma\left(\frac{1}{2}\right)=\sqrt{\pi} \)

Determine the indefinite integral \( \int (6x^3 + 4x^2) \, dx \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

(a) Determine whether \( f(x)=\frac{|x-4|-2}{x} \) is continuous at \( x=4 \). [6 marks] (b) Given \( f(x)=\frac{2 x}{\sqrt{x^{2}+2}} \). By finding the limit at appropriate values, obtain the horizontal and vertical asymptotes, if they exist. Hence, sketch the graphs of \( f(x)=\frac{2 x}{\sqrt{x^{2}+2}} \).