Tutor profile: Jason C.
Explain why you include a constant of integration every time you take an indefinite integral.
One way to look at it is that an indefinite integral ∫f asks for a solution to the differential equation F′(x)=f(x). That is, the function f(x) is given and you are looking for a function F(x) such that F′(x)=f(x). Now, it may be that a solution does not exist but if a solution does exist, say G(x) is found such that G′(X)=f(x) then for any constant C, the function G(x)+c is also a solution (just compute the derivative to see that). So the existence of a single solution implies the existence of infinitely many solutions. There is no particular reason to prefer one over the other so we indicate the entire family of solution by the (magical) '+C'.
Why are suppliers "price takers" in a perfectly competitive market?
Suppliers are "price takers" in a perfectly competitive market because they will sell at the market price. For instance, if one supplier decided to increase the price of a good, there would be no demand because demanders can get the same good for a cheaper price elsewhere. Additionally, if one supplier decided to decreased the price of the good, all other suppliers would be forced go to the same price (otherwise they would sell 0 products).
How come in free fall you feel weightless even though gravity is pulling down on you? (ignore air resistance when answering this question).
The reason you feel weightless is because there is no force pushing against you, since you are not in contact with anything. Gravity is pulling equally on all the particles in your body. This creates a sensation where no forces are acting on you and you feel weightless. It would be the same sensation as if you were floating in space.
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