Differentials Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-1/differentials/quiz/

1. 1

   Find dy for y = x² when x = 3 and dx = 0.1
   1. A) 0.06
   2. B) 6
   3. C) 0.6

2. 2

   Find dy for y = x² + 3x when x = 1 and dx = 0.01

   Answer: ____________________

3. 3

   Find dy for y = 2x² − x when x = 4 and dx = 0.05
   1. A) 15
   2. B) 0.75
   3. C) 7.5
   4. D) −0.75

4. 4

   Find dy for y = x² − 5x when x = 3 and dx = −0.1

   Answer: ____________________

5. 5

   Find dy for y = x³ − 2x when x = 2 and dx = 0.1, and compare with Δy
   1. A) 10
   2. B) −1
   3. C) 1
   4. D) 0.1

6. 6

   The cube has side 10 cm, measured with a possible error of 0.1 cm. Estimate the error in the volume.

   Answer: ____________________

7. 7

   The square has side 8 m, measured with a possible error of 0.1 m. Estimate the error in the area.

   Answer: ____________________

8. 8

   The circle has radius 8 cm, measured with a possible error of 0.1 cm. Estimate the error in the area.

   Answer: ____________________

9. 9

   The sphere has radius 5 cm, measured with a possible error of 0.1 cm. Estimate the error in the volume.
   1. A) 314.2 cm³
   2. B) 3.142 cm³
   3. C) 31.42 cm³

10. 10

    The cube has side 10 cm, measured with a possible error of 0.1 cm. Estimate the percentage error in the volume.

    Answer: ____________________