Formula

Tags

• Differential calculus
• Derivative
• Derivative formula
• Taylor polynomial
• Taylor

Detail

Explore the idea

Variables

• $x$Independent variable
• $a$Point or real constant
• $f$Function
• $n$Derivative order or exponent
• $k$Real constant

Frequently asked questions

What is the Taylor polynomial used for?

It approximates $f(x)$ near $a$ with a polynomial whose coefficients depend on the derivatives of $f$ at $a$. It is the foundation of power series in Calculus II.

Also known as

• Taylor series
• Taylor polynomial
• approximation

Related topics

• Taylor series

Related formulas

• Related

  Formula

  $$\frac{dy}{dt}=ky \quad\Longrightarrow\quad y(t)=y_0e^{kt}.$$
  Open formulaOpen in section

• Related

  Formula

  $$R_n(x)=\frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1},\qquad c\text{ between }a\text{ and }x,\ f^{(n+1)}\text{ exists and is continuous on the open interval between }a\text{ and }x$$
  Open formulaOpen in section

• Related

  Formula

  $$f(x)=P_n(x)+R_n(x)$$
  Open formulaOpen in section