2.1 Q-7

Q7. ${\lim }_{y\to 1}\frac{y^3-1}{y-1}$

\section*{Solution:} $\begin{array}{rl}& \underset{y\to 1}{\lim }\frac{y^3-1}{y-1}\\ & =\underset{y\to 1}{\lim }\frac{(y{)}^3-(1{)}^3}{y-1}\\ & =\underset{y\to 1}{\lim }\frac{(y-1)\left(y^2+y+1\right)}{y}\end{array}$ $\begin{array}{rl}& =\underset{y\to 1}{\lim }\left(y^2+y+1\right)\\ & =(1{)}^2+1+1\\ & =1+1+1\\ & =3\end{array}$