Question

The value of $\underset{x\to 1}{\lim }\frac{\sqrt[3]{(7-x)}-2}{(x+1)}$ is

• A. $-1/24$
• B. $-1/12$
• C. $1/36$
• D. $-36$

Answer 1

Answer: (B)

Let $x+1=h$
Then $\underset{x\to -1}{\lim }\frac{\sqrt[3]{(7-x)}-2}{(x+1)}$
$=\underset{h\to 0}{\lim }\frac{(8-h{)}^{1/3}-2}{h}$
$=\underset{h\to 0}{\lim }\frac{2{\left(1-\frac{h}{8}\right)}^{1/3}-2}{h}$
$=2\underset{h\to 0}{\lim }\frac{\left(1-\frac{1}{3}\frac{h}{8}\right)-1}{h}=-\frac{1}{12}$