details\nno additional details were added for this assignment.\nhw5 the limit laws (target l4; §2.3)\nscore…

details\nno additional details were added for this assignment.\nhw5 the limit laws (target l4; §2.3)\nscore: 3/13 answered: 3/13\nquestion 4\nevaluate the limit:\n\\(\\lim_{y\\to1}8y^{3}-4y =\\)\nquestion help: video message instructor

details\nno additional details were added for this assignment.\nhw5 the limit laws (target l4; §2.3)\nscore: 3/13 answered: 3/13\nquestion 4\nevaluate the limit:\n\\(\\lim_{y\\to1}8y^{3}-4y =\\)\nquestion help: video message instructor

Answer

Explanation:

Step1: Apply limit - sum/difference rule

$\lim_{y\rightarrow1}(8y^{3}-4y)=\lim_{y\rightarrow1}(8y^{3})-\lim_{y\rightarrow1}(4y)$

Step2: Apply constant - multiple rule

$=8\lim_{y\rightarrow1}(y^{3}) - 4\lim_{y\rightarrow1}(y)$

Step3: Use the power rule $\lim_{y\rightarrow a}y^{n}=a^{n}$ and $\lim_{y\rightarrow a}y = a$

$8\times1^{3}-4\times1$

Step4: Calculate the result

$8 - 4=4$

Answer:

$4$