Suman Saurav T.

You are planning to make an open rectangular box from an 8 -in.-by-15-in. piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of
the box of largest volume you can make this way, and what is its volume?

Consider a 100 -N weight suspended by two wires as shown in the accompanying figure. Find the magnitudes and components of the force vectors $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ .

(a) Write the area A of an equilateral triangle as a function of the side length s.
(b) Find the (instantaneous) rate of change of the area A with respect to a side s.
(c) Evaluate the rate of change of A at s " 2 and s " 10.
(d) If $s$ is measured in inches and $A$ is measured in square inches, what units would be appropriate for $d A / d s ?$

If $f$ and $g$ are both even functions, is $f+g$ even? If $f$ and $g$
are both odd functions, is $f+g$ odd? What if $f$ is even and
$g$ is odd? Justify your answers.

Two functions $f$ and $g$ can be combined by the arithmetic operations of _____,_____,_____,
and _____ to create new functions.

Finding an Inverse Function Informally In
Exercises $7-12$ , find the inverse function of $f$ informally.
Verify that $f\left(f^{-1}(x)\right)=x$ and $f^{-1}(f(x))=x$
$$f(x)=\frac{x-1}{5}$$