Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\overline{lim\ x-\sqrt{2-x^{2}}; 2x-\sqrt{2+2x^{2}}$$

Answer

$$-e^2*o*v*r*l^2*n*m*x-sqrt(2)-x^2;2*x-sqrt(2*(1+x^2))$$

Solution


Factor out the common term \(2\).
\[\begin{aligned}&overl\imath nel\imath mx-\sqrt{2}-{x}^{2}\\&2x-\sqrt{2(1+{x}^{2})}\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&ov{e}^{2}r{l}^{2}{\imath }^{2}nmx-\sqrt{2}-{x}^{2}\\&2x-\sqrt{2(1+{x}^{2})}\end{aligned}\]
Use Square Rule: \({i}^{2}=-1\).
\[\begin{aligned}&ov{e}^{2}r{l}^{2}\times -1\times nmx-\sqrt{2}-{x}^{2}\\&2x-\sqrt{2(1+{x}^{2})}\end{aligned}\]
Simplify  \(ov{e}^{2}r{l}^{2}\times -1\times nmx\)  to  \(ov{e}^{2}r{l}^{2}\times -nmx\).
\[\begin{aligned}&ov{e}^{2}r{l}^{2}\times -nmx-\sqrt{2}-{x}^{2}\\&2x-\sqrt{2(1+{x}^{2})}\end{aligned}\]
Regroup terms.
\[\begin{aligned}&-{e}^{2}ovr{l}^{2}nmx-\sqrt{2}-{x}^{2}\\&2x-\sqrt{2(1+{x}^{2})}\end{aligned}\]
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