Jika sudah memahami materi Inisiasi 5 , anda dapat mencoba berdiskusi mengenai soal di ba Tentukan persamaan garis singgung dari kurva \( x^{2} y^{2}+3 x y=10 y \) di titik (2,1). (gunakan turunan implisit)

nction définie par \( f(x)=\frac{L}{x^{2}+1} \)

(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 \( f(x)=\frac{2 x}{\sqrt{x^{2}+2}} \).

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

(1) Find the value of: \( \quad \lim _{x \rightarrow 4} \frac{x^{3}-15 x-4}{x-4} \)

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