Sam L.

asked • 04/06/20

Rate of change question

a block of ice melts in a room held at 70 degrees fahrenheit. Let f(t) be the base area of the block and g(t) the height of the block, measured with a ruler at time t.

a.) Assume the block of ice melts completely at time T. What values would you assign to f(T) and g(T)?

b.) Give physical reasons why lim as t-->T f(t)=f(T) and limt-->T g(t)=g(T) need not both hold: what are the limits?

c.) The limiting volume of the ice block at time T is zero. .Write this statement as a limit formula.

d.) Using (c.), illustrate the product rule for limits


Mark S.

a) 0. b) A physical aspect of the problem is whether or not the dimensions of the ice will shrink at the same rate. If they don't the limit of f(t) would not equal the limit of f(T) as t approaches T. And most likely they would not shrink at the same rate because of the thermal gradients in the air and nature in which ice cools. If the height is zero, the base area would also have to be zero. Regards, Mark S. Tutor on Wyzant's platform
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04/08/20

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