The Taylor series is used in calculus to represent a smooth function in the neighborhood of a point by a power series which is the limit of Taylor polynomials. This series expansion is called Taylor expansion. Series and development are named after the British mathematician Brook Taylor.
The calculator can be used to perform a Taylor series expansion on a function. The point around which the polynomial is developed can be moved on the graph. The recalculation is done after selecting the 'Update' button. In the definition of the function the parameters a, b and c can be used and varied by means of the sliders.
Development point
f(x) =
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Here are the derivations for the Taylor series elements:
If a function f(x) is differentiable enough times, it can be approximated by an nth order polynomial.
The Taylor series is:
Constants
Name | Description |
---|---|
LN2 | Natural logarithm of 2 |
LN10 | Natural logarithm of 10 |
LOG2E | Base 2 logarithm of EULER |
LOG10E | Base 10 logarithm of EULER |
PI | Ratio of the circumference of a circle to its diameter |
SQRT1_2 | Square root of 1/2 |
SQRT2 | Square root of 2 |
Trigonometric Functions
Function | Description |
---|---|
sin(x) | sine of x |
cos(x) | Cosine of x |
tan(x) | Tangent of x |
asin(x) | arcsine |
acos(x) | arccosine of x |
atan(x) | arctangent of x |
atan2(y, x) | Returns the arctangent of the quotient of its arguments. |
cosh(x) | Hyperbolic cosine of x |
sinh(x) | Hyperbolic sine of x |
Logarithm and Exponential
Function | Description |
---|---|
pow(x, y) | xy |
sqrt(x) | Square root of x |
exp(x) | ex |
log(x), ln(x) | Natural logarithm |
log(x, b) | Logarithm to base b |
log2(x), lb(x) | Logarithm to base 2 |
log10(x), ld(x) | Logarithm to base 10 |
More functions
Function | Description |
---|---|
ceil(x) | Get smallest integer n with n > x. |
abs(x) | Absolute value of x |
max(a, b, c, ...) | Maximum value of all given values. |
min(a, b, c, ...) | Minimum value of all given values. |
random(max = 1) | Generate a random number between 0 and max. |
round(v) | Returns the value of a number rounded to the nearest integer. |
floor(x) | Returns the biggest integer n with n < x. |
factorial(n) | Calculates n! |
trunc(v, p = 0) | Truncate v after the p-th decimal. |
V(s) | Returns the value of the given element, e.g. sliders and angles. |
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Here is a list of of further useful sites:
Index Curve fitting for: linear line, power function, polynomial, normal distribution Derivation rules Derivative calculator Gradient calculator Trigonometric calculations Normal Distribution Plot Fourier series calculator NxN Gauss method ODE first order General first order ODE