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2 years ago

Does anyone know which one it is ?

Mathematics

1 answer:

hammer [34]2 years ago

4 0

Answer:

The slope of the line is undefined

Step-by-step explanation:

The given line is a vertical line.

The slope of any vertical line is undefined.

Let us see why by using the slope formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

We substitute the coordinates of the points to obtain:

$m = \frac{3 - - 2}{1 - 1} = \frac{5}{0}$

This is not defined.

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

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Answer:

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

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

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

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

and the Taylor theorem with Lagrange remainder is

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Step-by-step explanation:

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