Precalculus by Richard Wright

Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own. Matthew 6:34 NIV

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.

- \(\displaystyle \lim_{x \rightarrow 2} \frac{x-2}{x^2+3x-10}\)
- \(\displaystyle \lim_{x \rightarrow 1} \frac{x^2+2}{x-4}\)
- \(\displaystyle \lim_{x \rightarrow 4} \frac{\sqrt{x}-2}{x-4}\)
- \(\displaystyle \lim_{x \rightarrow π} \frac{3}{\sin x}\)
- \(\displaystyle \lim_{x \rightarrow 2} \frac{x^3-8}{x-2}\)
*f*(*x*) = 4*x*+ 3*f*(*x*) = −3*x*^{2}- \(f(x) = -\frac{2}{x^2}\)
- Find the slope of \(f(x) = 2\sqrt{x}\) at (9, 6).
- \(\displaystyle \lim_{x \rightarrow ∞} \frac{x(2x+3)}{5x^2-7x+1}\)
- \(\displaystyle \lim_{x \rightarrow -∞} \frac{(2x+1)(3x-1)}{2x^3+5x-1}\)
- \(\displaystyle \lim_{x \rightarrow ∞} \frac{(2x-3)(5x^2+1)}{(x+1)(x-3)}\)
- \(a_n = \frac{7n^2-2n}{6n^2}\)
- \(a_n = \frac{2n+1}{4n^2}\)
*f*(*x*) = 5*x*^{2}−*x*[1, 3]*f*(*x*) = 2*x*[−1, 3]- 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.

Evaluate each limit.

Use a table or graph to find the limit to 4 decimal places. Draw the table or graph.

Find the derivative.

Find the limit at infinity.

Find the limit of the sequence.

Find the area between the graph and the *x*-axis for the given interval of *x*.

The equation *v* = −9.8*t* + 10 models the velocity of a ball thrown upwards at 10 m/s.

- \(\frac{1}{7}\)
- −1
- \(\frac{1}{4}\)
- Does not exist
- 12
*f*^{ –1}(*x*) = 4*f*^{ –1}(*x*) = –6*x*- \(f^{-1}(x) = \frac{4}{x^3}\)
- \(\frac{1}{3}\)
- \(\frac{2}{5}\)
- 0
- Does not exist
- \(\frac{7}{6}\)
- 0
- \(\frac{118}{3}\)
- 8
- −9.8 m/s
^{2} - −14.1 m