Meaning of "limit as h approaches 0"

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I am learning differentiation, and am having some trouble understanding what is meant by h approaching zero, from a positive or negative direction. If I understand correctly, h is one point on the secant line, and the other is x. The distance between the two of them is decreased, until the line is made tangent to the function f(x)=x^2. Why do we say, "as h approaches 0"? If x has a positive value, h will never come close to zero. What am I missing?

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1 Answer

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$h$ is not "one point on the secant line", it is the horizontal distance between the two points on the secant line. So saying "$h$ goes to $0$" means "Let the two points close in on eachother".

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