What is the difference between x and dx?

This response is based upon your having had some background in calculus. "dx" is not introduced before that.

Take a look at the sample function y = f(x) = x^2 + 9. Here x is the independent variable; the dependent variable y changes with x.

Now, for a big jump: we consider finding the area under a curve (graph) between x = a and x = b. We subdivide that interval [a,b] into n vertical slices of area. Each of those slices has its own area: f(x)*dx, where dx represents the width of such subarea. f(x)*dx is the actual subarea. To find the total area under the curve f(x) between x= a and x = b, we add up all of these individual subareas between x = a and x = b. Note that the subinterval width is

b-a

dx = , and that dx becomes smaller and smaller as the number of

n subintervals increases.

Once again, this all makes sense only if you've begun calculus (particularly integral calculus). Do not try to relate it to earlier math courses.

b. astronomers

b.my answer is b.

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