On a solid has cross sections perpendicular to the x-axis

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

0\le x\le 5

a solid has cross sections perpendicular to the x-axis. For

0\le x<2

the cross sections are squares whose side length is

4-x

units. For

2\le x\le 5

the cross sections are rectangles whose height is

x-1

units and whose width is the constant

k

units. Determine the value of

k

that makes the cross-sectional area continuous at

x=2