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Chapter 2: Q37E (page 77)

A warm can of soda is placed in a cold refrigerator. Sketch the graph of the temperature of the soda as a function of time. Is the initial rate of change of temperature greater or less than the rate of change after an hour?

Short Answer

Expert verified

Let the temperature of the soda be\(72^\circ {\rm{C}}\), and the temperature of the refrigerator is \(38^\circ {\rm{C}}\).

The Sooner, the can of soda, is placed in the refrigerator, the temperature of the can will initially decrease at a faster rate due to the large temperature difference. As the temperature difference reduces, the rate of change will also be less.

Step by step solution

01

Step 1:Write the variation in temperature

Let the temperature of the soda be\(72^\circ {\rm{C}}\), and the temperature of the refrigerator is \(38^\circ {\rm{C}}\).

The Sooner, the can of soda, is placed in the refrigerator, the temperature of the can will initially decrease at a faster rate due to the large temperature difference. As the temperature difference reduces, the rate of change will also be less.

02

Sketch the graph of temperature

The figure below represents the graph of the temperature of the can with respect to time.

Thus, the sketch of variation in the temperature is obtained.

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Most popular questions from this chapter

19-32: Prove the statement using the \(\varepsilon ,\delta \) definition of a limit.

31. \(\mathop {\lim }\limits_{x \to - 2} \left( {{x^2} - 1} \right) = 3\)

Find \(f'\left( a \right)\).

\(f\left( t \right) = {t^3} - 3t\)

For the function h whose graph is given, state the value of each quantity if it exists. If it does not exist, explain why.

(a)\(\mathop {{\bf{lim}}}\limits_{x \to - {{\bf{3}}^ - }} h\left( x \right)\)

(b)\(\mathop {{\bf{lim}}}\limits_{x \to - {{\bf{3}}^ + }} h\left( x \right)\)

(c) \(\mathop {{\bf{lim}}}\limits_{x \to - {\bf{3}}} h\left( x \right)\)

(d) \(h\left( { - {\bf{3}}} \right)\)

(e) \(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{0}}^ - }} h\left( x \right)\)

(f) \(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{0}}^ + }} h\left( x \right)\)

(g) \(\mathop {{\bf{lim}}}\limits_{x \to {\bf{0}}} h\left( x \right)\)

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(j) \(h\left( {\bf{2}} \right)\)

(k) \(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{5}}^ + }} h\left( x \right)\)

(l) \(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{5}}^ - }} h\left( x \right)\)

(a) The curve with equation\({\rm{2}}{y^{\rm{3}}} + {y^{\rm{2}}} - {y^{\rm{5}}} = {x^{\rm{4}}} - {\rm{2}}{{\rm{x}}^{\rm{3}}} + {x^{\rm{2}}}\)has been likened to a bouncing wagon. Use a computer algebra system to graph this curve and discover why.

(b) At how many points does this curve have horizontal tangent lines? Find the \(x\)-coordinates of these points.

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