Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #865 : Rate

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 4 and a rate of growth of 37?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 4 and a rate of growth of 37:

Example Question #866 : Rate

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 5 and a rate of growth of 36?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 5 and a rate of growth of 36:

Example Question #867 : Rate

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 6 and a rate of growth of 35?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 6 and a rate of growth of 35:

Example Question #781 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 7 and a rate of growth of 34?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 7 and a rate of growth of 34

Example Question #782 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 8 and a rate of growth of 33?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 8 and a rate of growth of 33:

Example Question #783 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 9 and a rate of growth of 32?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 9 and a rate of growth of 32:

Example Question #784 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 10 and a rate of growth of 31?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 10 and a rate of growth of 31:

Example Question #2661 : Functions

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 11 and a rate of growth of 30?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 11 and a rate of growth of 30:

Example Question #786 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 12 and a rate of growth of 29?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of its sides:

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 12 and a rate of growth of 29:

Example Question #787 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 12 and a rate of growth of 29?

Possible Answers:

Correct answer:

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rates of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 12 and a rate of growth of 29:

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