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3 years ago

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Exponential functions

2 answers:

Marysya12 [62]3 years ago

6 0

Answer:

2,323.23

Step-by-step explanation:

the interest will be 323.23 +your initial balance is what you will have in 5 years

Damm [24]3 years ago

6 0

In order to figure out the compound interest, you must first identify its equation which is: A = P(1+(r/n))^nt where A is the final amount, P is the initial amount, R is the interest rate, n is the number of times the interest is applied per period, and t is the number of periods. Plugging in your values would make the equation: A = 2000(1+(0.03/12))^(12•5) simplified would be A = 2323.23

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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

How do I solve 8 x 4 + 9 - 9 + 8

kap26 [50]

Answer:

Solution answer is 24

Step-by-step explanation:

=8 x 4 + 9 - 9 + 8

using D M A S rule

=32 + 9 - 9 +8

=41 - 17

=24

6 0

3 years ago

Read 2 more answers

Solve for x <br> A) -5<br> B) 6 <br> C) -9<br> D) 1

masha68 [24]

Answer:

Step-by-step explanation:

11 = 14+x+7+x

11=2x+21

2x=11-21=-10

X= -5

5 0

3 years ago

What is What is the measure of XYZ ?

ololo11 [35]

Answer:

The arc length, radius and the included angle are related as

r\theta=\widehat {XYZ} where \theta is in radians.

The radius r is given by

r=\frac{\widehat {XYZ} }{\theta} \\ r=\frac{10.8}{1.8} \\ r=6\;units

Correct choice is (B).

Step-by-step explanation:

6 0

4 years ago

Can anyone help me please

vladimir2022 [97]

A , because if you multiple you have to distribute

3 0

3 years ago

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