Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own. Matthew 6:34 NIV
12-Review
Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.
- Evaluate each limit.
- \(\displaystyle \lim_{x \rightarrow 2} \frac{x-2}{x^2+3x-10}\)
- \(\displaystyle \lim_{x \rightarrow 1} \frac{x^2+2}{x-4}\)
- \(\displaystyle \lim_{x \rightarrow 4} \frac{\sqrt{x}-2}{x-4}\)
- Use a table or graph to find the limit to 4 decimal places. Draw the table or graph.
- \(\displaystyle \lim_{x \rightarrow π} \frac{3}{\sin x}\)
- \(\displaystyle \lim_{x \rightarrow 2} \frac{x^3-8}{x-2}\)
- Find the derivative.
- f(x) = 4x + 3
- f(x) = −3x2
- \(f(x) = -\frac{2}{x^2}\)
- Find the slope of \(f(x) = 2\sqrt{x}\) at (9, 6).
- Find the limit at infinity.
- \(\displaystyle \lim_{x \rightarrow ∞} \frac{x(2x+3)}{5x^2-7x+1}\)
- \(\displaystyle \lim_{x \rightarrow -∞} \frac{(2x+1)(3x-1)}{2x^3+5x-1}\)
- \(\displaystyle \lim_{x \rightarrow ∞} \frac{(2x-3)(5x^2+1)}{(x+1)(x-3)}\)
- Find the limit of the sequence.
- \(a_n = \frac{7n^2-2n}{6n^2}\)
- \(a_n = \frac{2n+1}{4n^2}\)
- Find the area between the graph and the x-axis for the given interval of x.
- f(x) = 5x2 − x [1, 3]
- f(x) = 2x [−1, 3]
- The equation v = −9.8t + 10 models the velocity of a ball thrown upwards at 10 m/s.
- The derivative of velocity is the acceleration. Find the acceleration of the ball at t = 3 seconds.
- Displacement is the integral of the velocity graph. Find the displacement of the ball between t = 0 and t = 3 seconds.
Answers
- \(\frac{1}{7}\)
- −1
- \(\frac{1}{4}\)
- Does not exist
- 12
- f –1(x) = 4
- f –1(x) = –6x
- \(f^{-1}(x) = \frac{4}{x^3}\)
- \(\frac{1}{3}\)
- \(\frac{2}{5}\)
- 0
- Does not exist
- \(\frac{7}{6}\)
- 0
- \(\frac{118}{3}\)
- 8
- −9.8 m/s2
- −14.1 m
