True or false

If y =ax+b then DeltaY/DeltaX = dy/dx

If Y= x+c then dy = dx

If you can measure the length and width of a rectangle correct within .1 cm, then the calculated area will be correct within .1 cm as well.

I have True for the first 2 and false for the last one.

me too

You are correct on the first two statements:

1. If y = ax + b, then Δy/Δx = dy/dx. This is true because the derivative dy/dx can be interpreted as the average rate of change of y with respect to x, while Δy/Δx represents the change in y divided by the change in x.

2. If Y = x + c, then dy = dx. This is also true because the derivative represents the instantaneous rate of change, and for a linear function like Y = x + c, the rate of change of y with respect to x is always equal to 1.

As for the third statement:

3. If you can measure the length and width of a rectangle correctly within 0.1 cm, then the calculated area will be correct within 0.1 cm as well. This statement is false. The accuracy of the measured lengths of the sides does not necessarily guarantee the accuracy of the calculated area. The area of a rectangle is calculated by multiplying the length and width, and any errors or uncertainties in the measurements will propagate when calculating the area. Therefore, the precision of the calculated area may be influenced by the precision of the measurements.

You are correct with the first two statements but the last one is false. Let me explain why.

1. If y = ax + b, then Δy/Δx = dy/dx:
This statement is true. In calculus, dy/dx represents the derivative of y with respect to x, and Δy/Δx represents the average rate of change of y with respect to x over a small interval. In this case, since y = ax + b is a linear equation, the average rate of change Δy/Δx is equal to the derivative dy/dx.

2. If Y = x + c, then dy = dx:
This statement is false. Here, Y represents a linear equation, where c is a constant. In this scenario, dy does not equal dx. Instead, dy represents an infinitesimal change in y, and dx represents an infinitesimal change in x. Therefore, dy ≠ dx.

3. If you can measure the length and width of a rectangle correctly within .1 cm, then the calculated area will be correct within .1 cm as well:
This statement is false. The accuracy of measuring the length and width of a rectangle does not guarantee the same level of accuracy in calculating the area. The area of a rectangle is found by multiplying the length and width. Even if the length and width measurements are precise, any errors or deviations in the measurements will also be magnified when calculating the area. Consequently, the calculated area may not be correct within .1 cm if there are significant measurement errors.