Question

$\lim_{x \rightarrow a}\frac{f(x) - f(a)}{g(x) - g(a)},$

• A. $\frac{9}{100}$
• B. $- 1/2$
• C. $\frac{1}{99}$
• D. $\frac{1}{101}$

Answer 1

Answer: (B)

$- 1/2$

Answer 2

$= \lim_{n \rightarrow \infty}\frac{1}{n}\sum_{r = 1}^{n}{\left( \frac{r}{n} \right)^{99} = \int_{0}^{1}{x^{99}dx = \left\lbrack \frac{x^{100}}{100} \right\rbrack_{0}^{1} = \frac{1}{100}.}}$