Question

Find the vertical, horizontal, and oblique asymptotes, if any, for $f(x) = \frac{3x^3 + 20x^2 + 14x - 65}{x^2 + 8x + 15}$. vertical: $x = 5, x = 3$ slant: $y = 3x + 4$ vertical: $x = -5, x = -3$ slant: $y = 3x - 4$ vertical: $x = -5, x = 3$ horizontal: $y = 0$ horizontal: $y = 0$ slant: $y = 3x - 4$

Name: find the vertical horizontal and oblique asymptotes if any for fx frac3x3 20x2 14x 65x2 8x 15 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 horizontal y 0 hori 45035
Uploaded: 2024-08-01T12:14:26-08:00
Duration: 3 min 52 s
Channel: Adi S
Description: find the vertical horizontal and oblique asymptotes if any for fx frac3x3 20x2 14x 65x2 8x 15 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 horizontal y 0 hori 45035

          Find the vertical, horizontal, and oblique asymptotes, if any, for $f(x) = \frac{3x^3 + 20x^2 + 14x - 65}{x^2 + 8x + 15}$.
vertical: $x = 5, x = 3$
slant: $y = 3x + 4$
vertical: $x = -5, x = -3$
slant: $y = 3x - 4$
vertical: $x = -5, x = 3$
horizontal: $y = 0$
horizontal: $y = 0$
slant: $y = 3x - 4$

$find the vertical horizontal and oblique asymptotes if any for fx frac3x3 20x2 14x 65x2 8x 15 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 slant y 3x 4 vertical x 5 x 3 horizontal y 0 hori 45035$

Added by Nathan C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/01/2024

Step 1

The denominator is $x^2 + 8x + 15$. Set $x^2 + 8x + 15 = 0$. Factor the quadratic expression: We need two numbers that multiply to 15 and add to 8. These numbers are 3 and 5. So, $(x + 3)(x + 5) = 0$. This gives us two possible values for $x$: $x + 3 = 0 Show more…

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Find the vertical, horizontal, and oblique asymptotes, if any, for $f(x) = \frac{3x^3 + 20x^2 + 14x - 65}{x^2 + 8x + 15}$. vertical: $x = 5, x = 3$ slant: $y = 3x + 4$ vertical: $x = -5, x = -3$ slant: $y = 3x - 4$ vertical: $x = -5, x = 3$ horizontal: $y = 0$ horizontal: $y = 0$ slant: $y = 3x - 4$