To Compute y and dy
To find the values of y and dy using the formula y = 3x + 4x + 1, we first need to calculate y for each x value and then determine dy, which represents the change in y corresponding to a small change in x denoted by dx. The equation can be simplified to:
y = 7x + 1
Calculating y for given x values
Let’s find y for specific x values. Since the problem does not specify particular x values, we will compute y for chosen values (1, 2, 3).
- For x = 1:
y = 7(1) + 1 = 8
- For x = 2:
y = 7(2) + 1 = 15
- For x = 3:
y = 7(3) + 1 = 22
Calculating dy
To compute dy, we need the derivative of y with respect to x:
dy/dx = 7
Now, if we consider a small change in x, denoted as dx, the formula for dy becomes:
dy = (dy/dx) * dx = 7 * dx
To round our answers to three decimal places, if we choose a small dx, such as 0.1, we can compute dy:
If dx = 0.1:
dy = 7 * 0.1 = 0.7
In summary, we compute y based on x values, and dy is influenced by the choice of dx. For example:
- For x = 1,
y = 8,dy = 0.7 - For x = 2,
y = 15,dy = 0.7 - For x = 3,
y = 22,dy = 0.7
This method gives you a clear way to calculate and understand the relationship between y, dy, x, and dx effectively!