Find the value of $\lim_{x \to 96} \frac{x^2 - 96^2}{x - 96}$.
Using L'Hopital's rule or factoring: $(x^2 - 96^2)/(x - 96)$ = x + 96. At x = 96, limit = 192.
What is the derivative of $f(x) = x^97$ at x = 1?
f'(x) = 97 $x^{96}$. At x = 1, f'(1) = 97.
Consider the function f(x) = (x - $98)^2$. Which of the following statements are TRUE?
f(98) = 0, f'(98) = 0, f''(98) = 2 > 0 (so x = 98 is a local MINIMUM, not maximum).
Find the value of $\lim_{x \to 99} \frac{x^2 - 99^2}{x - 99}$.
Using L'Hopital's rule or factoring: $(x^2 - 99^2)/(x - 99)$ = x + 99. At x = 99, limit = 198.
What is the derivative of $f(x) = x^100$ at x = 1?
f'(x) = 100 $x^{99}$. At x = 1, f'(1) = 100.
