Hi everyone. I have a homework on numerical differentiation and I just want to know if my answers are correct.

1.) The partial derivative, of with respect toxis obtained by holdingyfixed and differentiating with respect tox.Similarly, is found by holdingxfixed and differentiating with respect toy.The equation below is adapted to partial derivatives:

[The two equations above are denoted as equation (i)]

(a). Let . Calculate the approximations to and using the formulas in (i) withh= 0.1, 0.01, and 0.001. Compare with the values obtained by differentiating

MY ANSWERS:

First, I solved for the derivative of with respect tox. I got:

Solving for using equation (i)

h_____ _ _____2h______

0.1_____1.23529____1.16327____0.20000___0.36014

0.01____1.20359____1.19639____0.20000___0.36000

0.001___1.20036____1.19964____0.20000___0.36000

Solving for

Derivative with respect to y:

Solving for using equation (i)

h_____ _ _____2h______

0.1_____1.21569____1.18367____0.20000___0.16006

0.01____1.20160____1.19840____0.20000___0.16000

0.001___1.20016____1.19984____0.20000___0.16000

Am I doing this right??

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2.) The distance traveled by an object is given in the table below:

_t_____D(t)

8.0___17.453

9.0___21.460

10.0__25.752

11.0__30.301

12.0__35.084

(a) Find the velocity by numerical differentiation

(b) Compare your answer with .

My Answers:

(a). Is it okay if I use central-difference to solve for the velocity? Or should I use forward of backward difference? If so, should I assume different step values (h)? Using central-difference, my answer is:

(b). .