Find the forward-difference for t = 0.2 in the following table.

Point 1 2 3 4 5
t 0 0.1 0.2 0.3 0.4
p(t) -2.00 -0.94 0.10 1.04 1.89

Round to 2 decimal place.

Question

Find the forward-difference for t = 0.2 in the following table.

Point	1	2	3	4	5
t	0	0.1	0.2	0.3	0.4
p(t)	-2.00	-0.94	0.10	1.04	1.89

Round to 2 decimal place.

BlackTom AI · Accepted Answer

To find the forward-difference approximation of the derivative at t = 0.2, we use the forward difference quotient: [p(t + h) − p(t)] / h, where h is the step size in t.

From the table, the t-values increase in increments of h = 0.1. For t = 0.2, we need p(0.3) and p(0.2):
- p(0.3) = 1.04
- p(0.2) = 0.10

Compute the forward difference in p: p(0.3) − p(0.2) = 1.04 − 0.10 = 0.94.

Now divide by h to obtain the forward-difference approximation to the derivative at t = 0.2:
0.94 / 0.1 = 9.4.

Therefore, the forward-difference value (the approximate derivative at t = 0.2) is 9.4 when rounded to two decimal places as requested.

As a check, note that if you only computed the simple forward difference in p without dividing by h, you would get 0.94, which is not the derivative approximation; dividing by h is the key step that yields 9.4. This distinction often causes confusion when people refer to 'forward difference' without specifying whether they mean the difference in p itself or the difference quotient that estimates the derivative.

In summary:
- h = 0.1
- p(0.3) − p(0.2) = 0.94
- [p(0.3) − p(0.2)] / h = 0.94 / 0.1 = 9.4
- Rounded to two decimals: 9.40, which is typically written as 9.4.

Find the forward-difference for t = 0.2 in the following table. Point 1 2 3 4 5 t 0 0.1 0.2 0.3 0.4 p(t) -2.00 -0.94 0.10 1.04 1.89 Round to 2 decimal place. 简答题

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