AP Calculus AB/BC FRQ Practice

♾️AP Calculus AB/BC

Practice FRQ 1 of 41/4

3. The following functions are defined for this question: $f(x) = \frac{x^2-4}{x-2}$ $g(x) = \frac{x^2-5x+6}{x-2}$ $h(x) = \frac{x^2-5x+6}{x(x-2)}$ $k(x) = -1$

Let $f$ be the function defined by $f(x)=\frac{x^2-4}{x-2}$ for $x≠ 2$ , and let $g$ be the function defined by $g(x)=\frac{x^2-5x+6}{x-2}$ for $x≠ 2$ . No graphing calculator is allowed for this question.

$f(x) = \frac{x^2-4}{x-2}$
$g(x) = \frac{x^2-5x+6}{x-2}$
$h(x) = \frac{x^2-5x+6}{x(x-2)}$
$k(x) = -1$

Approximate $f'(2)$ by interpreting the instantaneous rate of change at $x=2$ as an average rate of change over the interval $1.9≤ x≤ 2.1$ . Show the work that leads to your answer.

Write the limit $\lim_{x\to 2} g(x)$ in correct analytic notation and find its value. Show the algebraic work that leads to your answer.

A function $G$ is defined by $G(2)=k$ and $G(x)=g(x)$ for $x≠ 2$ . Find the value of $k$ such that $G$ is continuous at $x=2$ . Justify your answer using the definition of continuity at a point.

A new function $H$ is defined by $H(x)=\frac{g(x)}{x}$ for $x≠ 0,2$ . Find $\lim_{x\to\infty} H(x)$ and interpret the result as a horizontal asymptote of $H$ . For the function $H(x)=\frac{g(x)}{x}$ , analyze end behavior as $x\to\infty$ .

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