lineintegral1 said:You probably differentiated wrong or something similar. All you do is take the derivative of the potential function after you have integrated it in terms of x. Then you see if this matches the y component of your gradient. If they are the same, then the constant is zero. If they are not the same, then you integrate with respect to y.
Mark44 said:The problem says to "find a function f..."
All such functions are f(x, y) = (1/4)x4y4 + <some constant>
Since they're looking for just one, it's convenient to drop the constant.
The constant equals to 0 because it is a value that does not change and remains the same throughout an equation or experiment. It is used to represent a known or fixed quantity in a mathematical expression.
The significance of having a constant value of 0 is that it simplifies mathematical equations and makes them easier to solve. It also represents a state of equilibrium or balance in a system.
Yes, the constant can be a non-zero value in certain equations or experiments. It depends on the variables and factors involved in the specific situation. However, in many cases, using a constant of 0 can provide useful insights and simplify calculations.
A constant of 0 can affect the outcome of an experiment by either keeping the results constant or by cancelling out certain variables. It can also indicate that there is no relationship between two variables in the experiment.
Yes, there are many real-life examples of a constant equaling 0. For instance, the speed of light in a vacuum is a constant that equals 0. It also represents the freezing point of water at sea level. In economics, a 0% interest rate can be considered a constant for certain financial calculations.