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3 years ago

I need help.............

Mathematics

1 answer:

amid [387]3 years ago

7 0

I didn’t know which problem you specifically needed help with, but I hope this helps.

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EXAMPLE 2 Prove that 9ex is equal to the sum of its Maclaurin series. SOLUTION If f(x) = 9ex, then f (n + 1)(x) = for all n. If

amm1812

Answer:

To Prove: $9e^x$ is equal to the sum of its Maclaurin series.

Step-by-step explanation:

If $f(x) = 9e^x$ , then $f ^{(n + 1)(x)} =9e^x$ for all n. If d is any positive number and |x| ≤ d, then $|f^{(n + 1)(x)}| = 9e^x\leq 9e^d.$

So Taylor's Inequality, with a = 0 and M = $9e^d$ , says that $|R_n(x)| \leq \dfrac{9e^d}{(n+1)!} |x|^{n + 1} \:for\: |x| \leq d.$

Notice that the same constant $M = 9e^d$ works for every value of n.

But, since $lim_{n\to\infty}\dfrac{x^n}{n!} =0 $ for every real number x$$ ,

We have $lim_{n\to\infty} \dfrac{9e^d}{(n+1)!} |x|^{n + 1} =9e^d lim_{n\to\infty} \dfrac{|x|^{n + 1}}{(n+1)!} =0$

It follows from the Squeeze Theorem that $lim_{n\to\infty} |R_n(x)|=0$ and therefore $lim_{n\to\infty} R_n(x)=0$ for all values of x.

$THEOREM\\If f(x)=T_n(x)+R_n(x), $where $T_n $is the nth degree Taylor Polynomial of f at a and $ lim_{n\to\infty} R_n(x)=0 \: for \: |x-a|$

By this theorem above, $9e^x$ is equal to the sum of its Maclaurin series, that is,

$9e^x=\sum_{n=0}^{\infty}\frac{9x^n}{n!}$ for all x.

6 0

3 years ago

Help simplify please choose the correct answer~!!!!!

ANEK [815]

Answer:

Step-by-step explanation:

Given

-4x²(5 $x^{4}$ - 3x² + x - 2)

Multiply each term in the parenthesis by - 4x²

= - 20 $x^{6}$ + 12 $x^{4}$ - 4x³ + 8x²

7 0

3 years ago

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Solving Exponential Equations (lacking a common base)<br> (0.66)^k=9

Alexandra [31]

Answer:

k = log9 / log 0.66

k = 5.3

Step-by-step explanation:

Please always remember that, when an exponential equation is given with different bases, the best approach is to take log of both sides.

If you have a calculator handy, that would be pretty fast and easy.

0.66 ^ k = 9

Take log of both sides:

klog 0.66 = log 9

k = log 9 / log 0.66

k = 0.954 / - 0.18

k = -5.3

Maths is fun, let's keep learning

3 0

3 years ago

Simplify by combining like terms 5/6a+4 1/4a

algol [13]

Answer:

61/12a

Step-by-step explanation:

convert the mixed number 4 1/4 into a improper fraction which turns into 17/4, you then add the sum of 5/6a + 17/4a which is 61/12a

7 0

3 years ago

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HELP Increase 1 by 10%

jek_recluse [69]

Answer:

1.1

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

I need help.............​

I need help.............