Answer:
The polynomial is an approximation with an error less than or equals to <em>0.002652</em> for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
According to Taylor's theorem
with
for some c in the interval (-x, x)
In the particular case f
<em>f(x)=cos(x)
</em>
<em>
</em>
we have
therefore
and the polynomial approximation of T5(x) of cos(x) would be
In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that
for some c in (-x,x). So
and we must find the values of x for which
Working this inequality out, we find
![\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652\Rightarrow |x|^6\leq1.90944\Rightarrow\\\\\Rightarrow |x|\leq\sqrt[6]{1.90944}\Rightarrow |x|\leq1.113826815](https://tex.z-dn.net/?f=%5Cbf%20%5Cdisplaystyle%5Cfrac%7B%7Cx%7C%5E6%7D%7B6%21%7D%5Cleq0.002652%5CRightarrow%20%7Cx%7C%5E6%5Cleq1.90944%5CRightarrow%5C%5C%5C%5C%5CRightarrow%20%7Cx%7C%5Cleq%5Csqrt%5B6%5D%7B1.90944%7D%5CRightarrow%20%7Cx%7C%5Cleq1.113826815)
Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
x = hours Ali was charged for
150 + 50 x = 375
- 150 -150
50x = 225
÷ 50. ÷50
x = 4.5 hours
Find the intersection of the following sets.<br><br>a= 1,2,3,4,5,6,7,8 b= 2,4,6,8,10<br>
Neporo4naja [7]
{2,4,6,8}
Intersection means common elements in both sets
Do you mean <span><span><span><span>cos6</span>x+6<span>cos4</span>x+15<span>cos2</span>x+10</span><span><span>cos5</span>x+5<span>cos3</span>x+10cosx</span></span> ?</span>
or <span><span><span>cos6x+6cos4x+15cos2x+10</span><span>cos5x+5cos3x+10cosx</span></span> ?</span>
or <span><span><span><span>cos6</span>x+6<span>cos4</span>x+15<span>cos2</span>x+10</span><span><span>cos5</span>x</span></span>+5<span>cos3</span>x+10cosx ?</span>
or <span><span><span>cos6x+6cos4x+15cos2x+10</span><span>cos5x</span></span>+5cos3x+10cosx <span>?</span></span>
Mean and Median best describe the typical number of minutes she spent reading each day.
