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2 years ago

What is the midpoint between 10 & 20

Mathematics

1 answer:

-Dominant- [34]2 years ago

5 0

The mid point in between 10&20 is 15

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Use scientific notation to calculate the exact number of hours in one year

Mrrafil [7]

8.7 x 10^3

The total number of hours in one year is 8760

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3 years ago

use Taylor's Theorem with integral remainder and the mean-value theorem for integrals to deduce Taylor's Theorem with lagrange r

Vadim26 [7]

Answer:

As consequence of the Taylor theorem with integral remainder we have that

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt$

If we ask that $f$ has continuous $(n+1)$ th derivative we can apply the mean value theorem for integrals. Then, there exists $c$ between $a$ and $x$ such that

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x$

Hence,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .$

Thus,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$

and the Taylor theorem with Lagrange remainder is

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$ .

Step-by-step explanation:

5 0

2 years ago

What is -14=k+9?

Basile [38]

Answer:

k = -23

Step-by-step explanation:

-14=k+9

Subtract 9 from each side

-14-9 = k+9-9

-23 = k

7 0

3 years ago

Read 2 more answers

Find the product of (p+5)(p-2)

Korolek [52]

Answer:

The answer is p^2+3p-10

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2 years ago

Cameron earns $7 per hour. How much does he earn in 5 hours

ANEK [815]

All you have to do is multiply both

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3 years ago