Question

Solve : $\underset{x\to 1}{lim}\frac{x^{431}+3.x^{221}-2.x^{39}-2}{x-1}=$

Answer 1

${lim}_{x\to 1}\frac{x^{431}+3x^{321}-2x^{39}-2}{x-1}$

Applying L'Hospitals rule

${lim}_{x\to 1}\frac{431x^{430}+\left(321\right)3x^{320}-\left(39\right)2x^{38}-0}{1-0}$

${lim}_{x\to 1}431x^{430}+\left(321\right)3x^{320}-\left(39\right)2x^{38}$

$=431+(3\times 321)-(2\times 39)$

$=1316$