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djyliett [7]
3 years ago
5

Please help me with this question ​

Mathematics
1 answer:
leva [86]3 years ago
7 0

Answer:

I believe the answer is B

Step-by-step explanation:

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Find T5(x) : Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0 . (You need to enter function.) T5(x)= Find all va
Burka [1]

Answer:

\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}

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

\bf f(x)=f(0)+f'(0)x+f''(0)\displaystyle\frac{x^2}{2}+f^{(3)}(0)\displaystyle\frac{x^3}{3!}+f^{(4)}(0)\displaystyle\frac{x^4}{4!}+f^{(5)}(0)\displaystyle\frac{x^5}{5!}+R_6(x)

with

\bf R_6(x)=f^{(6)}(c)\displaystyle\frac{x^6}{6!}

for some c in the interval (-x, x)

In the particular case f

<em>f(x)=cos(x) </em>

<em> </em>

we have

\bf f'(x)=-sin(x)\\f''(x)=-cos(x)\\f^{(3)}(x)=sin(x)\\f^{(4)}(x)=cos(x)\\f^{(5)}(x)=-sin(x)\\f^{(6)}(x)=-cos(x)

therefore

\bf f'(x)=-sin(0)=0\\f''(0)=-cos(0)=-1\\f^{(3)}(0)=sin(0)=0\\f^{(4)}(0)=cos(0)=1\\f^{(5)}(0)=-sin(0)=0

and the polynomial approximation of T5(x) of cos(x) would be

\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}

In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that

\bf R_6(x)=-cos(c)\displaystyle\frac{x^6}{6!}

for some c in (-x,x). So

\bf |R_6(x)|\leq|\displaystyle\frac{x^6}{6!}|=\displaystyle\frac{|x|^6}{6!}

and we must find the values of x for which

\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652

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

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]

8 0
3 years ago
What is the value of X
kozerog [31]

Answer:

x = 20

Step-by-step explanation:

The triangle is isosceles ( 2 congruent sides )

Hence the base angles are congruent, thus

3x = 60 ( divide both sides by 3 )

x = 20

4 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE HELP I NEED HELP WITH THIS :((<br> i will give brainliest:)
bezimeni [28]

-3+8=5

2-6=-4

-3+-1=-4

4 0
3 years ago
Elizabeth uses 23.25 ounces of granola and 10.5 ounces of raisins for 15 servings of trail mix.If each serving contains the same
alexdok [17]
The answer is 2.22 if you divide it. Add the ingredients then divide on how many servings.
5 0
3 years ago
Read 2 more answers
1
AfilCa [17]

Answer:

(A) Your friend will save $282.

(B) Your friend will get 23.5% off the original price of the mattress.

Step-by-step explanation:

We first need to find out the price of the mattress after the 15% discount. Our first step is to find what 15% of 1,200 is. We can do this by multiplying the two numbers.

1,200 x 15% -----> 1,200 x 0.15= 180.

15% of $1,200 is $180.

Next subtract $180 from $1,200, which equals $1,020. We can now apply the 10% off internet coupon.

1,020 x 10% ------> 1,020 x 0.10= 102.

10% of $1,020 is $102.

Next we subtract $102 from $1,020 and we get $918, the final price of the discounted mattress.

We subtract to see how much money the friend saved.

$1,200 - $918= $282.

We can get the percentage by dividing $282 by $1,200.

282 / 1200= 0.235 decimal form ----> 23.5%

6 0
2 years ago
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