   Chapter 9.1, Problem 43E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 45-48, use the table feature of a graphing calculator to predict each limit. Check your work by using either a graphical or an algebraic approach. lim x →  -  ∞ x 4 − 4 x 2 x 2 + 8 x + 12

To determine

The value of limx2x44x2x2+8x+12, using the TABLE feature of calculator. Also, check the limit.

Explanation

Given Information:

The limit is limx2x44x2x2+8x+12.

Explanation:

Consider the provided limit,

limx2x44x2x2+8x+12

To find limit of above function, use the Ti-83 graphing calculator for its TABLE feature.

Step 1: Open the Ti-83 graphing calculator and press ON key.

Step 2: Press the [Y=] key and enter the function in Y1, Y1=((x4)4x2)/(x2+8x+12).

Step 3: Press the [2nd] key then the [WINDOW] key and adjust the value of TbleStart=2.4 and set “Indpnt” at Ask and “Depend”

at Auto.

Step 4: Press the [2nd] key and then the [GRAPH] key.

XY12.47.042.25.3492.0014.00624.0011.93.4341.82.931

Consider the provided limit,

limx2x44x2x2+8x+12

The limit from the left is represented by limx2f(x) and the limit from the right is represented by limx2+f(x).

The limxcf(x) will exist at c=2 when the limit from the left, that is, the values of f(c) but c<2, is equal to the limit from the right, that is, the values of f(c) but c>2.

From the table,

limx2f(x)4

And,

limx2+f(x)4

Since,

limx2f(x)=limx2+f(x)

Hence, the value of limx2x44x2x2+8x+12 is 4

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