What is X in a Maclaurin series?
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What is X in a Maclaurin series?
A Maclaurin series is a power series that allows one to calculate an approximation of a function f ( x ) f(x) f(x) for input values close to zero, given that one knows the values of the successive derivatives of the function at zero. In many practical applications, it is equivalent to the function it represents.
What is the expansion of log 1 x?
log(1+x)=x – x2/2 + x3/3 – x4/4 + …. The easiest way to see it is by using an integral representation. integrating term by term gives the series for log(1+x), where the integration limits are [0,x].
Where can I find Maclaurin series expansion?
A Maclaurin series is a function that has expansion series that gives the sum of derivatives of that function. The Maclaurin series of a function $f(x)$ up to order n may be found using Series $[f, {x, 0, n}]$. f(x)=f(x0)+f′(x0)(x−x0)+f”(x0)2!…Maclaurin Series Formula.
| Function | Maclaurin Series |
|---|---|
| $ln(1+x)$ | ln(1+x)=∑∞n=1(−1)n+1xnn=x−x22+x33−⋯ |
What is the difference between Maclaurin and Taylor series?
In the field of mathematics, a Taylor series is defined as the representation of a function as an infinite sum of terms that are calculated from the values of the function’s derivatives at a single point. A Maclaurin series is the expansion of the Taylor series of a function about zero.
How do you know if a Maclaurin series converges?
Remember, the alternating series test tells us that a series converges if lim n → ∞ a n = 0 \lim_{n\to\infty}a_n=0 limn→∞an=0. Because the limit is 0, the series converges by the alternating series test, which means the Maclaurin series converges at the left endpoint of the interval, x = − 1 / 2 x=-1/2 x=−1/2.
What is the derivative of log 1 x?
Calculus Examples To apply the Chain Rule, set u u as 1x 1 x . The derivative of log(u) log ( u ) with respect to u u is 1uln(10) 1 u ln ( 10 ) .
What is the series of log X?
Logarithmic series: modified First, the series of log(l – x) was a succession of powers of x divided by the harmonic succession of integral numbers, alternating in sign. The series for log(l – x) uses the same numerical terms, but all the signs are minus.