This presentation gives idea about Taylor and Maclaurian Series with examples.

1. Taylor and Maclaurin Series
Prepared By : Sandip Panchal
Made By : Harsh Pathak
Subject : Calculus

2. CONTENT
• INTODUCTION
• DEFINIATION of Taylor Series
• DEFINIATION of Maclaurin Series
• Examples

3. INTODUCTION
• Taylor series is a representation of a function as an infinite sumvof terms
that are calculated from the values of the function's derivatives at a single
point.
• The concept of a Taylor series was formulated by the Scottish
mathematician James Gregory and formally introduced by the English
mathematician Brook Taylor in 1715. If the Taylor series is centered at
zero, then that series is also called a Maclaurin series, named after the
Scottish mathematician Colin Maclaurin , who made extensive use of this
special case of Taylor series in the 18th century.

4. DEFINIATION of Taylor Series
• The Taylor series of a real or complex-valued
function f ( x ) that is infinitely differentiable
at a real or complex number a is the power
series

5. DEFINIATION of Maclaurin Series
• A Maclaurin series is a Taylor series expansion
of a function about 0,

6. Examples
Example 1 : Expand √x in powers of (x-1)

7. Example 2: Find the Maclaurin series for sinx