Homework SourseHomework 3 P14 1 2 3 4 SolutionWe have fx 3x2 2x 4 an
Homework 3 P14
| 1. | ![\"g(1)\"](\"//webwork.utpa.edu/wwtmp/equations/e5/27b7c7d9c45331484c49d5b95048a81.png\") | = | |
| 2. | ![\"g(0.1)\"](\"//webwork.utpa.edu/wwtmp/equations/c4/b8e9572a5da366f68a0d6532959f361.png\") | = | |
| 3. | ![\"g(0.01)\"](\"//webwork.utpa.edu/wwtmp/equations/fc/dc9548baf200ef8340674955da2a7b1.png\") | = | |
| 4. | ![\"g(0.001)\"](\"//webwork.utpa.edu/wwtmp/equations/3e/ee291a2282ea9093cfd992ddf80eb71.png\") | = |
Solution
We have f(x) = 3x2 + 2x + 4 and g(h) = [f (3 + h) -f ( 3 )]/h . Then f (3) = 3(3)2 + 2*3 + 4 = 27 + 6 + 4 = 37. Also f (4) = 3(4)2 + 2*4 + 4 = 48+ 8 + 4 = 60; f (3.1) = 28.83 + 6.2 + 4 = 39.03; f ( 3.01) = 27.1803 + 6.02 + 4 = 37.2003 ; f ( 3.001) = 27.018003 + 6.002 + 4 = 37.020003
Then g(1) = [f (3 + 1) -f ( 3 )]/1 = [f (4) -f ( 3 )]/1 = 60 - 37 = 23 , g (0.1) = [f (3.1) - f ( 3 )]/0.1 = (39.03 - 37)/ 0.1 = 20.3; g ( 0.01) = [f (3.01) - f ( 3 )]/0.01 = (37.2003 - 37) / 0.01 = 20.03; g ( 0.001) = [f (3.001) - f ( 3 )]/0.001 = ( 37.020003 - 37)/ 0.001 = 20.0003. These results are tabulated below:
The values of g are getting closer and closer to 20. Therefore, L = 20
| 1. | g(1) | = | 23 |
| 2. | g(0.1) | = | 20.3 |
| 3. | g (0.01) | = | 20.03 |
| 4. | g (0.001) | = | 20.0003 |
![Homework 3 P14 1. = 2. = 3. = 4. = SolutionWe have f(x) = 3x2 + 2x + 4 and g(h) = [f (3 + h) -f ( 3 )]/h . Then f (3) = 3(3)2 + 2*3 + 4 = 27 + 6 + 4 = 37. Also](/WebImages/19/homework-3-p14-1-2-3-4-solutionwe-have-fx-3x2-2x-4-an-1041857-1761541300-0.webp "Homework 3 P14 1. = 2. = 3. = 4. = SolutionWe have f(x) = 3x2 + 2x + 4 and g(h) = [f (3 + h) -f ( 3 )]/h . Then f (3) = 3(3)2 + 2*3 + 4 = 27 + 6 + 4 = 37. Also")
