Math Problem Statement

Söylev this equtıon with this rules

Söylev this equtıon with this rules

Solution

It seems that you've uploaded two images containing mathematical expressions and examples related to Taylor Series and approximations. The first image involves finding the Taylor Series expansions for functions such as x\sqrt{x} at x=4x=4, ln(x)\ln(x) at x=1x=1, and sin(x)\sin(x) at x=0x=0. The second image provides more insight into the procedure for finding these expansions, including the use of derivatives at specific points and how to apply the general formula for Taylor Series.

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Math Problem Analysis

Mathematical Concepts

Taylor Series
Polynomial Approximation
Derivatives
Limits

Formulas

T_n(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2 / 2! + ... + f^(n)(a)(x-a)^n / n!

Theorems

Taylor's Theorem
Polynomial Approximation

Suitable Grade Level

Grades 11-12