{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1996BC1

# 1996BC1 - 96 BC-l Consider the graph of the function it...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 96: BC-l Consider the graph of the function it given by h(x) : 3‘12 for 0 S x < so. (a) Let R be the unbounded region in the first quadrant below the graph of It. Find the volume of the solid generated when R is revolved about the y—axis. (b) Let A(w9 be the area of the shaded rectangle shown in the figure to the right. Show that A(w) has its maximum value when w is the x-coordinate of the point of inflection of the graph of h A (a) V =21: 1;} 0010min: =21tfo°°xe "2dr (cylindrical shells) = 21: lim bxe ”‘de (u = -x2, du = —2xdr, —~;-du =xdx) b—poo 0 = -1tiim ‘bze"du= —nlim (9" b-ooo 0 b~+oo :2) = "11 lim(e“l'2 ~e°) =11: © b—>oo (13) 1400 = we “"2 =9. gig =A'(w) = —22w2e‘w2 + e““’1 = e“"’z(-2w2 + 1) W e-W‘(—2w2+t)=0 ==> -2w2+1=0 m} w= % ”(t/E) =0, A'(w) >0 on (On/E) and A’(w) <0 on (goo) =>Ahasanabsolute maximum atw=g,w>0 * h’(x) = ~2xe"2 x; h”(x) = -2(—2x2e 1“ + e"2 = e2e"2(—2x2 + 1) mg) =0, h”(x) <0 on (OW/E) and h”(x) >0 on (goo) ==>hhasapointofinﬂeotionatx= % * © 1996 BC} ...
View Full Document

{[ snackBarMessage ]}