Please generate answers to questions #13,17,19 in pics.

Please show all work.

13. a. A company makes computer chips from square wafers of silicon. A process engineer wants to keep the side length of a wafer very close to 15 mm and needs to know how the area A(a:) of a wafer changes when the side length 3: changes. Find 3: changes. Find A' (15) and explain its meaning in this situation. SHOW ANSWER b. Show that the rate of change of the area of a square with respect to its side length is half its perimeter. Try to explain geometrically Why this is true by drawing a square Whose side length a: is increased by an amount A3: . How can you approximate the resulting change in area AA if Am is small? 17. A spherical balloon is being inated. Find the rate of increase of the surface area (S : 4W2) with respect to the radius 7' when 7' is a. 1 ft, 1). 2 ft, and c. 3 ft. What conclusion can you make? 19- The mass of the part of a metal rod that lies between its left end and a point :13 meters to the right is 3:}:2 kg. Find the linear density (see Example 2) when a: is a. 1 m, h. 2 m, and c. 3 m. Where is the density the highest? The lowest