How do you find vertical, horizontal and oblique asymptotes for #f(x)=(5x^2-x+3)/(x+3)#?

Answer 1

Vertical asymptote is #x =-3#
No horizontal asymptote
Oblique asymptotes is #y=5x-16#

An ASYMPTOTE is a line that approches a curve, but NEVER meets it.

To find the vertical asymptote , put the denominator = 0 (because 0 cannot divide any number) and solve.

Given below is the step-by-step walk through

The curve will never touch the line #x=-3#, thereby making it the vertical asymptote.

Next, we find the horizontal asymptote:
Compare the degree of the expressions in the numerator and the denominator.
Since the degree in the numerator is greater than the degree in the denominator, there are no horizontal asymptote.

The oblique asymptote is a line of the form y = mx + c.
Oblique asymtote exists when the degree of numerator = degree of denominator + 1

To find the oblique asymptote divide the numerator by the denominator.

The quotient is the oblique asymptote.
Therefore, the oblique asymptote for the given function is #y=5x-16#.

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Answer 2

To find the vertical asymptotes, set the denominator equal to zero and solve for x. In this case, x + 3 = 0, so x = -3. This gives us a vertical asymptote at x = -3.

To find the horizontal asymptote, compare the degrees of the numerator and denominator. The degree of the numerator is 2 and the degree of the denominator is 1. Since the degree of the numerator is greater, there is no horizontal asymptote.

To find the oblique asymptote, divide the numerator by the denominator using polynomial long division. This will give you a quotient and a remainder. The quotient will represent the oblique asymptote.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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