glasskerfu
2021-01-19
Answered

Perform the indicated divisions.

$\frac{{x}^{2}-7x-78}{x+6}$

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Cristiano Sears

Answered 2021-01-20
Author has **96** answers

Division of a polynomial by binomial is done by long-division method.

In this method to find the first quotient term, divide the first dividend term by the first divisor term.

Multiply the divisor with the term obtained by dividing the first dividend term with the first quotient term.

The product obtained is subtracted from the dividend.

Repeat the same process to divide the other terms of the dividend.

Calculation:

Consider the polynomial

The following steps are used to solve the problem.

First multiply the divisor by x and write the product

The value obtained is equals to —13x.

Now multiply the divisor by -13 and write the product —13x — 78 under the dividend and simplify.

The polynomial

Then,

The simplified value of the polynomial

Final statement:

The simplified value of the polynomial after division is equals to (x — 13).

Final statement:

The simplified value of the polynomial after division is equals to (x-13).

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Find $\underset{x\to 0}{lim}\left(\frac{\mathrm{ln}(\mathrm{cos}x)}{x\sqrt{1+x}-x}\right)$ efficiently

Now, it looked to me like a classic L'Hôpital's rule case. Indeed, I used it (twice), but then things became messy and complicated.

Am I missing the point of this exercise? I mean, there must be a "nicer" way. Or should I stick with this road?

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Regarding Yiorgos's answer: Why is the following true?

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Now, it looked to me like a classic L'Hôpital's rule case. Indeed, I used it (twice), but then things became messy and complicated.

Am I missing the point of this exercise? I mean, there must be a "nicer" way. Or should I stick with this road?

EDIT:

Regarding Yiorgos's answer: Why is the following true?

$\mathrm{ln}(1-\frac{{x}^{2}}{2})\approx -\frac{{x}^{2}}{2}$

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