Taylor Polynomials
Graphs a function
f(
x) and the Taylor polynomial approximations
to
f(
x) up to degree 4
for a given
c value (the center point for the Taylor polynomials).
How to use
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Examples
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Other Notes
Try the Derivative Calculator.
How to use
- Enter a function f (x) in the text input field
marked "f (x)="
(Example:
f (x)=ex)
- Click the "Graph" button
(this button also refreshes the graph)
- Enter the derivativs
f '(x),
f '(x), etc.,
in the text input fields
marked
"f '(x)=",
"f ''(x)=", etc. (up to the fourth derivative)
(Example:
f '(x)=f ''(x)=...=ex)
- Select a c value, the center point for the Taylor polynomials
(Example:
c=1)
This can be done in either of two ways:
- Click and drag the mouse on the graph -- value of c
corresponds to horizontal mouse position on graph
- Enter the value in the text input field marked "c="
and click the
"Graph" button to refresh
- To erase the graph and all input fields, click the
"Clear" button
The text input fields marked "f (x)=",
"f '(x)=", etc., can accept
a wide variety of expressions to represent functions.
The text input field marked "c="
can accept a real number in decimal
notation. The
buttons under the graph
allow various manipulations of
the graph coordinates.
For assistance computing the derivatives
f '(x),
f ''(x), etc.,
try the Derivative Calculator.
Examples
Exponential:
f (x) = ex
f '(x) = ex
f ''(x) = ex
f '''(x) = ex
f ''''(x) = ex
c = 1
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Trigonometric:
f (x) = sin x
f '(x) = cos x
f ''(x) = -sin x
f '''(x) = -cos x
f ''''(x) = sin x
c = 0
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Other Notes
The degree one Taylor polynomial (tangent line)
will be shown in blue,
degree two in red,
degree three in green,
and degree four in orange.