Question

$$lim_{x\rightarrow\pi}\frac{2x^{2}-6x\pi+4m^{2}}{x^{2}-\pi^{2}}$$

Answer

$$l<-PI(2*x^2-6*PI*x+4*m^2)/(IM*m*x*(x^2-PI^2))$$

Solution


Regroup terms.
\[l\imath mx->\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{{x}^{2}-{\pi }^{2}}\]
Regroup terms.
\[-+l\imath mx>\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{{x}^{2}-{\pi }^{2}}\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{{x}^{2}-{\pi }^{2}}}{\imath }\]
Simplify  \(\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{{x}^{2}-{\pi }^{2}}}{\imath }\)  to  \(\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath ({x}^{2}-{\pi }^{2})}\).
\[-+lmx>\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath ({x}^{2}-{\pi }^{2})}\]
Divide both sides by \(m\).
\[-+lx>\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath ({x}^{2}-{\pi }^{2})}}{m}\]
Simplify  \(\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath ({x}^{2}-{\pi }^{2})}}{m}\)  to  \(\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath m({x}^{2}-{\pi }^{2})}\).
\[-+lx>\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath m({x}^{2}-{\pi }^{2})}\]
Divide both sides by \(x\).
\[-+l>\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath m({x}^{2}-{\pi }^{2})}}{x}\]
Simplify  \(\frac{\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath m({x}^{2}-{\pi }^{2})}}{x}\)  to  \(\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath mx({x}^{2}-{\pi }^{2})}\).
\[-+l>\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath mx({x}^{2}-{\pi }^{2})}\]
Multiply both sides by \(-1\).
\[l<-\frac{\pi (2{x}^{2}-6\pi x+4{m}^{2})}{\imath mx({x}^{2}-{\pi }^{2})}\]