Use increments to make the required estimate.RADIATION Stefan’s law in physics states that...

Use increments to make the required estimate.

RADIATION Stefan’s law in physics states that a body emits radiant energy according to the formula R(T) = kT4, where R is the amount of energy emitted from a surface whose temperature is T(in degrees kelvin) and k is a positive constant. Estimate the percentage change in R that results from a 2% increase in T.

Newton’s Method■ Tangent line approximations can be used in a variety of ways. Newton’s method for approximating the roots of an equation f(x) = 0 is based on the idea that if we start with a “guess” x0 that is close to an actual root c, we can often obtain an improved estimate by finding the x intercept x1 of the tangent line to the curve y = f(x)at x = x0(see the figure). The process can then be repeated until a desired degree of accuracy is attained. In practice, it is usually easier and faster to use the ZOOMand TRACEfeatures of your graphing utility to find roots, but the ideas behind Newton’s method are still important. Exercises 33 through 37 involve Newton’s method.