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)

Show that \( F(x)=|x| \) is continuous everywhere.

11. Find the values of \( a \) and \( b \) that make \( f \) continuous everywhere. \[ f(x)=\left\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & \text { if } x<2 \\ a x^{2}-b x+3 & \text { if } 2 \leq x<3 \\ 2 x-a+b & \text { if } x \geq 3\end{array}\right. \]

USing first principle prove that \( y=\sin x \) then \( \frac{d y}{d x}=\cos x \)

8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \).

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.