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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 2.2 / Problem 70E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Chapter 2, Problem 70E

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QUESTION:

PROBLEM 70E

You will find a graphing calculator useful

Let

a. Make a table of the values of h at the points x = 2.9, 2.99, 2.999, and so on. Then estimate . What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,….instead?

b. Support your conclusions in part (a) by graphing h near x0 = 3 and using Zoom and Trace to estimate y-values on the graph as x → 3

c. Find algebraically.

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QUESTION:

PROBLEM 70E

You will find a graphing calculator useful

Let

a. Make a table of the values of h at the points x = 2.9, 2.99, 2.999, and so on. Then estimate . What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,….instead?

b. Support your conclusions in part (a) by graphing h near x0 = 3 and using Zoom and Trace to estimate y-values on the graph as x → 3

c. Find algebraically.

ANSWER:

Solution

Step 1 of 4

In this problem we have to make the table of $h$ and estimate $\lim\limits_{{x} \rightarrow {3}}H(x)$ and also draw the graph of as $x\rightarrow{}3.$

Given that $h(x)=\frac{{x}^{2}-2x-3}{{x}^{2}-4x+3}$

(a)

The table of the function is

Value of x	$h(x)=\frac{{x}^{2}-2x-3}{{x}^{2}-4x+3}$
2.9	2.052631
2.99	2.005025
2.999	2.000500
2.9999	2.000050
2.99999	2.000005
2.99999	2.0000005

As x approaches 3 from left side as $h(x)$ approaches 2

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