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3 years ago

May can swim one lap in 6.089 seconds, and Sarah can swim one lap in 6.098 seconds. Write an equation to compare their speeds.

Mathematics

2 answers:

Pie3 years ago

6 0

6.098-6.089=.009 maybe?

lord [1]3 years ago

5 0

Speed,v= distance,d/time,t
v=d/6.089..........May
v=d/6.098..........Sarah
this makes it turn out to be a simultaneous equation, so you could move on from here

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2 years ago

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We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

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Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

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