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Delta is a symbol used in mathematics and science that represents change. For example, delta y over delta x means the change in y over the change in x.
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delta t is change in temperature
It is the rate of change at one given moment, and it is the same as the value of the derivative at a particular point. The point may be thought of as that given moment. When we talk about functions, the instantaneous rate of change at a point is the same as the slope, m, of the tangent line.. Sometimes we think of it as the slope of the curve. The best way to understand this is with the difference quotient and limits. The difference quotient is the average rate of change of y with respect to x. If we then look at the difference quotient and we let delta x ->0, this will be the instantaneous rate of change. In other words, the time interval gets smaller and smaller. Difference quotient is delta y/ delta x where delta represents the change.
For each delta > 0 there exists some epsilon > 0 such that: |x - y| < epsilon ensures that |f(x) - f(y)| < delta.