1.The length and width of a rectangle are both varying over time. Assume that the diagonal of the rectangle remains constant at 5ft, and that the width is increasing at a rate of 0.5 ft/min. When the width is 4 ft long, and length is 3 ft long, how fast is the length of the rectangle changing at that time?

2.Let f be the function defined by f(x) = ln(9 x^2).

1)Find the domain of f.

2) Find the linear approximation of f at 2.

3.Find f the derivative of the following functions. Do not simplify your answers.

1) f(x) = log3[((2x + 1)]

2) f(x) = [e^tan(5x)]/10^x

3) f(x) =[ (7^3x) +(x^7)]^10