Math 180 Name _________________ Summer 2013
Homework #1 Due Wednesday, June 26
No late papers accepted! No excuses!
1. Solve each equation or inequality. a) 2x 3 4 b) sin 3x( ) = cos 3x( ) 0,2[ ] c) 32 x1 = 5x+2 d) log2 x + log2 x 2( ) = 3
e) cos +1= sin 0,2[ ] f) 3xex + x2ex = 0
g) ex 12ex 1= 0 h) 5x3 x2 4x + 4 0
2. A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 x . One piece is bent into the shape of a square and the other piece of wire is bent into the shape of a circle. Find a function that models the total area enclosed. State the domain of your function.
3. A rectangle is inscribed in a circle of radius 4. Find a function that models the
area of the rectangle as a function of x.
4. Carol has 2400 feet of fencing to fence in three adjacent rectangular pens. a) Find a function that models the total area of the pens. b) Find the domain. c) Find the dimensions of the pens that will maximize the area.
5. Let f x( ) = x2 4 . Find f x + h( ) f x( )h