91Ó°ÊÓ

Area Suppose that the radius \(r\) and area \(A=\pi r^{2}\) of a circle are differentiable functions of \(t\) . Write an equation that relates \(d A / d t\) to \(d r / d t .\)

Estimating volume Estimate the volume of material in a cylindrical shell with length 30 in... radius 6 in. and shell thickness 0.5 in.

The radius \(r\) of a circle is measured with an error of at most 2\(\%\) . What is the maximum corresponding percentage error in computing the circle's $$\text{a. circumference?} \quad \text{b. area?}$$

Quadratic tangent to identity function The curve \(y=\) \(a x^{2}+b x+c\) passes through the point \((1,2)\) and is tangent to the line \(y=x\) at the origin. Find \(a, b,\) and \(c .\)