You do not have to. Could start with sum = 10 and initial value of 4, but then your formulae may be less easy to work with.
I suggest: - Take the derivative of the function - Find its initial value, which could be done with the initial value theorem That value is the slope of the original function.
divide 100 by the initial value and times by the new value, then take 100 from the total.
No. Closed means that you could do the operation (division) on any two natural numbers and you would get a result in the natural numbers. Take 7/3 for example, this is obviously not a natural number.
Yes Natural Numbers are often described as "counting numbers". You can certainly count to 9015 (although it will take you a while) so 9015 is a natural number.
No. But there can be more than one data point which has the same value as the mean for the set of numbers. Or there can be none that take the mean value.
By using the rise over run formula: (y2-y1)/(x2-x1) This means you need two points on the line in order to solve for the slope. You take the y-value for the second point and then subtract the y-value from the initial point. Then divide that by the x-value of the second point minus the x-value from the initial point.
For an even number of values, there will be 2 middle numbers. Take the average of the 2 middle numbers for the median. It will be a value not in the data set.
The shooting method is a method of reducing a boundary value problem to an initial value problem. You essentially take the first boundary condition as an initial point, and then 'create' a second condition stating the gradient of the function at the initial point and shoot/aim the function towards the second boundary condition at the end of the interval by solving the initial value problem you have made, and then adjust your gradient condition to get closer to the boundary condition until you're within an acceptable amount of error. Once within a decent degree of error, your solution to the initial value problem is the solution to the boundary value problem. Have attached PDF file I found which might explain it better than I have been able to here.
Natural numbers are sometimes defined to include zero, sometimes not. Equivalent terms therefore may include: positive integers, non-negative integers, whole numbers, positive whole numbers ("whole number" is ambiguous; some take it to include negative numbers, some not).
The simplest is to take their average. So, if A and B are two numbers, then (A + B)/2 is halfway between them.
No because for example the reciprocal of 2 is 1/2
An initial reaction is like a first take in of everything.