Cảu 4 Giá tri \( \lim _{x \rightarrow 0} \sqrt{2 x^{2}+7} \) bằng \( \begin{array}{llll}\text { A. } 5 & \text { B. } \sqrt{19} & \text { C. } 7 & \text { D. } 3 \sqrt{2}\end{array} \)

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( 1.2 .2 \quad f(x) \) non real. \( 1.2 .3 \quad f(x) \) undefined \( 1.2 .4 \quad f(x)>0 \) Simplify: \( \quad \frac{2^{x}-2^{-x}}{4^{x}-1} \)

Find the exact area of the resulting surface obtained by rotating about the y-axis the curve: \( y=\frac{1}{3} x^{\frac{3}{2}}, 0 \leq x \leq 12 \).

Find \( \frac{d^{2} y}{d x^{2}} \) given that \( x^{3}-3 x y+y^{3}=1 \)

Q1. Find the values of a and b such that the surface: \( a x^{2}-b y z=(a+2) x \) and \( 4 x^{2} y+z^{3}=4 \) cut orthogonally at \( (1,-1,2) \)

\( \int ^ { 3 A 3 } ( 3 ^ { x } - 3 ^ { 2 } ) : 3 + 3 ^ { 3 } : 3 ^ { 2 } = \)