AP Calculus Review Worksheet

AP Calculus Review Worksheet

Read each question carefully and provide your answer in the space provided. Show all your work for full credit.

1. Evaluate the limit: $\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$

2. Find the derivative of the function $f(x) = 3x^4 - 2x^2 + 5x - 1$ with respect to $x$.

3. The antiderivative of $f(x) = \cos(x)$ is  .

4. The power rule for integration states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq$  .

5. If a function is differentiable at a point, then it is continuous at that point.

6. A particle's position is given by $s(t) = t^3 - 6t^2 + 9t$, where $t$ is in seconds and $s(t)$ is in meters. Find the velocity of the particle at $t=2$ seconds.

7. For the function $f(x) = x^3 - 3x^2 + 2$, identify the intervals where the function is increasing and decreasing.