How can I compute the values of y and dy for the given values of x and dx in the expression y = 3x + x^2 + 3x + 0.6, rounding the results to three decimal places?

To compute y and dy for the given expression y = 3x + x^2 + 3x + 0.6, we first simplify the equation:

• Combine like terms: y = 6x + x^2 + 0.6.

Next, we need to substitute the provided values of x and dx. For this example, let’s assume:

• x = 1
• dx = 0.1

Now, we will calculate y:

• y = 6(1) + (1)^2 + 0.6 = 6 + 1 + 0.6 = 7.6

Next, we must find dy, which represents the differential of y. This can be computed using the derivative of y with respect to x:

• First, find the derivative: dy/dx = 6 + 2x.
• Substituting the value of x = 1: dy/dx = 6 + 2(1) = 8.

Now, we can calculate dy as follows:

• dy = (dy/dx) * dx
• dy = 8 * 0.1 = 0.8

Finally, rounding both results to three decimal places:

• y: 7.600
• dy: 0.800

To summarize:

• Computed value of y: 7.600
• Computed value of dy: 0.800

This method allows for consistent calculation of both y and dy based on the given values of x and dx.