The document presents an overview of Taylor's and Maclaurin's series, explaining how these mathematical concepts represent functions as infinite sums derived from their derivatives at a specific point. It includes a formal definition for the Taylor series and details about its components such as derivatives and factorials. Additionally, the presentation features various layouts summarizing task descriptions, class group data, and content organization.

1. CALCULUS
AND ANALYTICAL
GEOMETRY

2. Presented by Group no. 02:
 Abdul Fatir
 Aiman Malik
 Shehzadi Manal
Presented to:Ma’am Hina Zahid

3. TAYLOR’S SERIES

4. MACLAURIN’S SERIES
 The Taylor series is a mathematical representation of a function as an infinite sum of terms, each
derived from the function's derivatives at a single point. The series approximates the function in
the vicinity of that point.
 Definition
For a function f(x)f(x)f(x), the Taylor series centered at aaa is given by:
f(x)=f(a)+f′(a)(x a)+f′′(a)2!(x a)2+f′′′(a)3!(x a)3+
− − − ⋯
Or, in summation form:
f(x)= n=0 f(n)(a)n!(x a)n
∑ ∞ −
 where:
 f(n)(a)f^{(n)}(a)f(n)(a) is the n-th derivative of f(x)f(x)f(x) evaluated at a,
 n! is the factorial of n,
 a is the point around which the series is centered

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