MTH 514 Lecture 25: mth514l25

State the derivative of each function.

(a)   

(b)   

(c)   

(d)   

(e)   

(f)   

(g)   

(h)   

(i)   

(j)   

(k)   

(l)   

(m)   

let L:u-v and M:V-W be linear mappings.

a) show if L,M are injective , then ML is injective

b) show if L,M are surjective , then ML is surjective

The length l, width w, and height h of abox change with time. At a certain instant the dimensions arel = 5 m and w= h= 4 m, and l and w are increasing at a rate of 3 m/swhile h is decreasing at a rate of 6 m/s. At that instantfind therates atwhich the following quantities arechanging.