Mathematics, 09.10.2019 21:50 IzzybellaRamilo

The slant asymptote for x^3-2x^2+x-4/x^2+1 is y=x-2

true or false?

The slant asymptote for x^3-2x^2+x-4/x^2+1 is y=x-2true or false?

Answers: 3

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Answer from: peno211

Option 1. T

Step-by-step explanation:

The given function is f(x)= $\frac{x^{3}-2x^{2}+x-4}{x^{2}+1}$

and the statement states that slant asymptote of the the function is y = x-2

We have to evaluate the statement is true or false.

Now to find the slant asymtote we will divide the numerator by denominator.

We get the function in the form of $f(x)= (x-2)-(\frac{2}{x^{2}+1})$

By ignoring the fraction part we can say that the expression which represents the slant asymptote is (x -2).

Therefore the given statement is true.

Answer from: smithjirrah

True. The slant asymptote is y=x-2

Step-by-step explanation:

A slant asymptote is the equation of a line of the form y = mx + b

Where m is the slope and b is the cut point with the y axis.

To find these asymptotes, you must make the following limit:

$m = \lim_{x \to \infty}\frac{f(x)}{x}$

$b = \lim_{x \to \infty}[f(x) -mx]$

With the given function f(x) we make the first limit to find the slope of the line:

$m= \lim_{x \to \infty}\frac{\frac{x^3-2x^2+x-4}{x^2+1}}{x}$

$m= \lim_{x \to \infty}\frac{x^3-2x^2+x-4}{x^3+x}$

We divide each term between x ^ 3

$m= \lim_{x \to \infty}\frac{1-0 + 0 -0}{1+0}$

m = 1

Now we solve the second limit

$b = \lim_{x \to \infty}[\frac{x^3-2x^2+x-4}{x^2+1}-x]\\\\b = \lim_{x \to \infty}[\frac{x^3-2x^2+x-4 -[x^3+x]}{x^2+1}]\\\\b = \lim_{x \to \infty}[\frac{-2x^2-4}{x^2+1}]\\\\b = \lim_{x \to \infty}[\frac{-2\frac{x^2}{x^2}-\frac{4}{x^2}}{\frac{x^2}{x^2}+\frac{1}{x^2}}]\\\\\\b = -2$

Finally: The slant asymptote is y = x-2

Answer from: Quest

The answer is b) 32 your welcome

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

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The slant asymptote for x^3-2x^2+x-4/x^2+1 is y=x-2

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