question 11 evaluate the limit $lim_{y \to 2}\frac{5(y^{2}-1)}{79(y - 1)^{3}}$
question 11 evaluate the limit $lim_{y \to 2}\frac{5(y^{2}-1)}{79(y - 1)^{3}}$
Answer
Explanation:
Step1: Substitute (y = 2) into the function
We have the limit (\lim_{y\rightarrow2}\frac{5(y^{2}-1)}{7y(y - 1)^{3}}). First, calculate (y^{2}-1) and ((y - 1)^{3}) when (y = 2). For (y^{2}-1), when (y=2), (y^{2}-1=2^{2}-1=4 - 1=3). For ((y - 1)^{3}), when (y = 2), ((y - 1)^{3}=(2 - 1)^{3}=1).
Step2: Calculate the value of the whole - function
Substitute the above - calculated values into the original limit. The original limit becomes (\frac{5\times3}{7\times2\times1^{3}}). [ \begin{align*} \frac{5\times3}{7\times2\times1}&=\frac{15}{14} \end{align*} ]
Answer:
(\frac{15}{14})