Chapter 12 Infinite series, improper integrals, and Taylor series
... In studying calculus, we have explored a variety of functions. Among the most basic are polynomials, i.e. functions such as p(x) = x5 + 2x2 + 3x + 2. These functions have features that make them particularly easy to handle: it is elementary to compute the derivatives and integrals of polynomials. Fu ...
... In studying calculus, we have explored a variety of functions. Among the most basic are polynomials, i.e. functions such as p(x) = x5 + 2x2 + 3x + 2. These functions have features that make them particularly easy to handle: it is elementary to compute the derivatives and integrals of polynomials. Fu ...
Week 6
... of differentiation allow you to calculate the derivative of any algebraic expression. You calculate integrals by trial and error using the rules of differentiation. There are many integrals that cannot be expressed using elementary functions. The cumulative normal N (z) is one of the best known. Thi ...
... of differentiation allow you to calculate the derivative of any algebraic expression. You calculate integrals by trial and error using the rules of differentiation. There are many integrals that cannot be expressed using elementary functions. The cumulative normal N (z) is one of the best known. Thi ...
An algorithm for computing a neighborhood
... that f ðx0 Þ ¼ 0. The next section shows how such a proof can be done by combining interval computation with algebra calculus. 3. Sufficient condition to check f >0. This section proposes a theorem which provides a sufficient condition to check the following assertion for a given differentiable real v ...
... that f ðx0 Þ ¼ 0. The next section shows how such a proof can be done by combining interval computation with algebra calculus. 3. Sufficient condition to check f >0. This section proposes a theorem which provides a sufficient condition to check the following assertion for a given differentiable real v ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.