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Paul
August 7, 2018

Calculus I - Assignment Problems
 Derivatives Previous Chapter Next Chapter Integrals Linear Approximations Previous Section Next Section Newton's Method

## Differentials

For problems 1  5 compute the differential of the given function.

1.

2.

3.

4.

5.

5. Compute dy and  for  as x changes from 6 radians to 6.05 radians.

6. Compute dy and  for  as x changes from -2 to -2.1.

7. Compute dy and  for  as x changes from 3 to 3.02.

8. Compute dy and  for  as x changes from -10 to -9.99.

9. The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inches.  What is the maximum possible error in the surface area of the cube if we use this value of the length of the side to compute the surface area?

10. The radius of a circle is found to be 7 cm in length with a possible error of no more than 0.04 cm.  What is the maximum possible error in the area of the circle if we use this value of the radius to compute the area?

11. The radius of a sphere is found to be 22 cm in length with a possible error of no more than 0.07 cm.  What is the maximum possible error in the volume of the sphere if we use this value of the radius to compute the volume?

12. The radius of a sphere is found to be  foot in length with a possible error of no more than 0.03 inches.  What is the maximum possible error in the surface area of the sphere if we use this value of the radius to compute the surface area?

 Linear Approximations Previous Section Next Section Newton's Method Derivatives Previous Chapter Next Chapter Integrals

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