Question

A block of ice melts in a room held at 75◦F. 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 t→T f(t) = f(T) and lim t→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

Answer 1

a) At time T, block melts completely, so at time T, height of block will become zero and complete volume will be spreaded on floor which will become base area now, so base area will become equal to volume of block.So, f(T) = Volume of block and g(T) = 0

b) Because while melting, it is possible that ice does not melt for a long time and it suddenly melts, so in this case limit will be different. Therefore, itt is possible that both limits does not hold. This is possible physical reason.

c)

  

d)