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In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
Therefore, the expression on the right-hand side is just the equation for the tangent line to the graph of at (, ()). For this reason, this process is also called the tangent line approximation . Linear approximations in this case are further improved when the second derivative of a, f ″ ( a ) {\displaystyle f''(a)} , is sufficiently small ...
The quotient and remainder may be computed by any of several algorithms, including polynomial long division and synthetic division. [19] When the denominator b(x) is monic and linear, that is, b(x) = x − c for some constant c, then the polynomial remainder theorem asserts that the remainder of the division of a(x) by b(x) is the evaluation a ...
Envelope theorem (calculus of variations) Equal incircles theorem (Euclidean geometry) Equidistribution theorem (ergodic theory) Equipartition theorem (ergodic theory) Erdős–Anning theorem (discrete geometry) Erdős–Dushnik–Miller theorem ; Erdős–Gallai theorem (graph theory) Erdős–Ginzburg–Ziv theorem (number theory)
Natural gas futures surged 24% with a cold spell expected across the eastern half of the US. Forecasts call for below-average temperatures on the East Coast and parts of the Midwest for January.
Netanyahu is among older world leaders including President Biden, 82, President-elect Donald Trump, 79, and Pope Francis, 88, who have come under scrutiny for their age and health issues.
Remainder theorem may refer to: Polynomial remainder theorem; Chinese remainder theorem This page was last edited on 29 December 2019, at 22:03 (UTC). Text is ...
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