Question

$$\lim _ { x \rightarrow 1 } \frac { \sqrt { \sqrt { 3 x ^ { 2 } + 1 } + 2 } - 2 } { x - 4 } ; \lim _ { x \rightarrow - }$$

Answer

$$3*IM*l*m*x^2+1+2-2*x-4;;l*IM*m*xBo*x+33$$

Solution


Use this rule: \({\sqrt{x}}^{2}=x\).
\[\begin{aligned}&l\imath mx\times 1\times 3x+1+2-2x-4\\&\\&l\imath mxBox+33\end{aligned}\]
Regroup terms.
\[\begin{aligned}&3lmxx\imath +1+2-2x-4\\&\\&l\imath mxBox+33\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&3lm{x}^{2}\imath +1+2-2x-4\\&\\&l\imath mxBox+33\end{aligned}\]
Regroup terms.
\[\begin{aligned}&3\imath lm{x}^{2}+1+2-2x-4\\&\\&l\imath mxBox+33\end{aligned}\]