1.01: Introduction to Numerical Methods

Mathematisa | Math Animations on Instagram: "✨The Taylor series (or Taylor expansion) of a function is an infinite sum that represents a function like e^x or cos(x) in terms of its derivatives at a single point. When the expansion is at 0, it’s called a Maclaurin series. The sum of the first n+1 terms forms the nth Taylor polynomial, which is a polynomial approximation of the function. As n increases, the approximation becomes more accurate. Taylor's theorem provides estimates of the error in th

SOLVED:A different kind of approximation When approximating a function f using a Taylor polynomial, we use information about f and its derivative at one point. An alternative approach (called interpolation) uses information about f at several different points. Suppose we wish to approximate f(x)=sinx on the interval [0, π]. a. Write the (quadratic) Taylor polynomial p2 for f centered at π/ 2. b. Now consider a quadratic interpolating polynomial q(x)=a x^2 b x c . The coefficients a, b, and c are