Department of Mathematics and Statistics s1

School of Mathematical and Statistical Sciences Arizona State University Mat 267 Engineering Calculus III

Your name: First Last

Project 1: Due by February 25, 2011 Friday Solve the following problems and submit your work and clearly write your first and last name. Print this page and use as a cover page.

1. Find the equation of the tangent line to y=1 + 4sin x at (0, 1).

2. The figure shows a sector of a circle with central angle x, let A( x ) be the area of the segment between the chord PR and the arc PR . Let B( x ) be the area of the A( x ) triangle PQR, find lim P x 0+ B( x ) A(x) B(x) x O Q R

3. Find the negative value of K so that the curve y= x2 -2 x + 7 has the tangent line y= Kx + 5 , find exact value of K, no decimal no rounding.

4. Find the volume of the solid that lies inside both the spheres x2+ y 2 + z 2 +4 x - 2 y + 4 z + 5 = 0 and x2+ y 2 + z 2 = 4 . No decimal, produce exact answer.