   Chapter 3.4, Problem 42E

Chapter
Section
Textbook Problem

# (a) Graph the function f ( x ) = 2 x 2 + 1 3 x − 5 How many horizontal and vertical asymptotes do you observe? Use the graph to estimate the values of the limits lim x →   ∞ 2 x 2 + 1 3 x − 5    and    lim x →   − ∞ 2 x 2 + 1 3 x − 5 (b) By calculating values of f(x) , give numerical estimates of the limits in part (a).(c) Calculate the exact values of the limits in part (a). Did you get the same value or different values for these two limits? [In view of your answer to part (a), you might have to check your calculation for the second limit.]

To determine

(a)

To find:

i. Graph of function fx=2x2+13x-5

ii. Number of horizontal and vertical asymptotes observed

iii. Estimate values of limits limx2x2+13x-5 and limx-2x2+13x-5

Explanation

1) Concept:

Use the definition of horizontal and vertical asymptote

2) Definitions:

Horizontal asymptote:

Horizontal asymptote: y=b

As x±, yb or limx±∞ f(x)=b

Vertical asymptote:

Vertical asymptote: x=c

As xc, y± or limxcf(x)=±

3) Given:

fx=2x2+13x-5

4) Calculation:

i. Graph of function fx=2x2+13x-5 is

ii. From the graph vertical asymptote is at x1.7 and horizontal asymptote at y0.5 and y- 0.5

iii

To determine

(b)

To give:

Numerical estimates to the limits in part (a) by calculating values of f(x)

To determine

(c)

To find:

The exact value of limits in part (a)

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