AP Calculus BC 1.5: Algebraic Properties of Limits

Practise AP Calculus BC 1.5 by applying limit laws to sums, quotients and composite functions, and comparing one-sided limits to decide whether a limit exists.

Exam points

Use table values and limit laws to evaluate quotients and composite functions at a target input.
Compare left- and right-hand limits of absolute-value expressions to decide whether a two-sided limit exists.

[Maximum number: 1]

The functions f(x), g(x), and h(x) have derivatives of all orders. Listed above are values for the functions and their first and second derivatives at x=3. Find $\lim _{x \rightarrow 3} \frac{(f(x))^{2}-3 h(x)}{g(x)+h(x)}$ .

$-\frac{1}{5}$

$\frac{1}{2}$

nonexistent

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LIM-1.D—Determine the limits of functions using limit theorems question 1