Following is the list of letter grades for students in an algebra class:

$$\begin{array}{ccc} \hline A & B & F & A &C & C & A & B & D\\ F & D & A & A & B & C & F & B & D\\ C & A & A & A & F & B & C & A & C\\ \hline \end{array}$$

Construct a relative frequency distribution for these data.

In this exercise, use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative.

$$f(x)=\sqrt{x}(2-x)^2$$

Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \

$$f(x)=\sqrt{x}(2-x)^2$$

This exercise should be done using a graphing calculator or computer algebra system. Plot

$$f ( x ) = \cos \left( x ^ { 2 } \right) \sin x$$

for

$$0 \leq x \leq 2 \pi.$$

Then illustrate local linearity at x = 3.8 by choosing appropriate viewing rectangles.

If the curve $y=e^{-x / 10} \sin x, x \geqslant 0$, is rotated about the x-axis, the resulting solid looks like an infinite decreasing string of beads. Find the exact volume of the nth bead. (Use either a table of integrals or a computer algebra system.)

One of the two antiderivatives can be determined using basic algebra and the antiderivative formulas we have presented. Name the method by finding the antiderivative of this one and label the other “N/A.” (a) $\int 2 \sec x d x$, (b) $\int \sec ^{2} x d x$

Use a computer algebra system to analyze the function over the given interval.
Find any relative extrema and points of inflection. \

$$f(x)=\sin x-\dfrac{1}{3} \sin 3 x+\dfrac{1}{5} \sin 5 x,[0, \pi]$$

In the following exercise, use a computer algebra system to graph the pair of intersecting lines and find the point of intersection.

$$x=2 t+3, y=5 t-2, z=-t+1$$

$$x=-2 s+7, y=s+8, z=2 s-1$$

In Exercises I through $22$, find the critical points of the given fianctions and classify each as a relative maximum, a relative minimum, or a saddle point. (Note: The algebra in Exercises $19$ through $22$ is challenging.)

$$f(x, y)=5-x^2-y^2$$

In this exercise, use a computer algebra system and the error formulas to find $n$ such that the error in the approximation of the definite integral is less than $0 . 0 0 0 0 1$ using the Trapezoidal Rule.

$$\int_0^1 \sin x^2 d x$$

In the given exercise, evaluate the integral using the appropriate method or combination of methods covered thus far in the text. Use the integral tables at the end of the text, but do not use a computer algebra system.

$$\displaystyle \int \sec ^5 y \tan y d y$$

In the given exercise, evaluate the integral using the appropriate method or combination of methods covered thus far in the text. Use the integral tables at the end of the text, but do not use a computer algebra system.

$$\displaystyle \int \tan ^5 x \sec x d x$$

In the given exercise, evaluate the integral using the appropriate method or combination of methods covered thus far in the text. Use the integral tables at the end of the text, but do not use a computer algebra system.

$$\displaystyle \int \sqrt{x^4+x^7} d x$$

Use a computer algebra system to evaluate the following integral. Find both an exact result and an approximate result for each definite integral. Assume a is a positive real number. $\int\left(a^{2}-t^{2}\right)^{-2} d t$