Power series with Real Coefficients. The exponential function (in blue), and the sum of the first n + 1 terms… Radius of convergence. A power series will converge for some values of the variable x… Operations on power series. Power Series
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Category: AP
Derivative test
First Derivative Test for Local Extrema. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. Second Derivative Test. 1. If , then has a local minimum at . 2. If , then has a local maximum at . The extremum test gives slightly more general conditions under which […]
First Principle Method
First principle method for differentiation. The gradient of the secant and the gradient of the tangent We can put this more precisely and more usefully. Derivative by First Principle. A derivative is simply a measure of the rate of change. It can be the rate of change of distance with respect to time or the temperature with […]
Second Fundamental Theorem of Calculus
First fundamental theorem of calculus
First fundamental theorem of calculus If we define an area function, F (x), as the area under the curve y=f (t) from t=0 to t=x, then the area function in this case is F (x)=c∗x. The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation Theorem of Calculus of integration
