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Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m/s and its downward acceleration...

The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm.   (a) Use differentials to estimate the maximum error in the calculated surface area.   What...

When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of...

In the viewing rectangle [-4, 4] by [-20, 20], graph the function f(x) = x^3 - 3x and its secant line through the points (-3, -18) and (3, 18). Find the values of the numbers c that satisfy...

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x) = cos 2x, [π/8,...

A particle moves according to a law of motion below 0 <= t < 12, where t is measured in seconds and s in feet.   s= f(t) = cos(tpi/6)     (a) Find the total...

(a) The volume V of a growing spherical cell is V = 4/3 pi r^, where the radius is measured in micrometers (1 µm = 10^-6m). Find the average rate of change of V with respect to r when r changes...

A particle moves according to a law of motion below, 0 ≤ t < 12, where t is measured in seconds and s in feet.    s = f(t) =cos(tpi/6)   (a) Find the total distance...