Answered: Use a graphing utility to graph the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = (−x² − 3x − 1)/(x − 2)

Expert Solution

Step 1

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

We have to:

(i) To draw The sketch of the curve.

(ii) To find the slant asymptote of the curve.

(iii)Why does the slant asymptote occur?

Step 2

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

To find the slant asymptote we will divide this rational function and then, using the quotient, we will get the equation of the slant asymptote.

Since,

$x - 2) - x^{2} - 3 x - 1 (- x - 5 - x^{2} + 2 x - 5 x - 1 - 5 x + 10 - 11$

The quotient is -x - 5. Thus, the equation of the slant asymptote is $g (x) = - x - 5$ .

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