For each function, create your own table of values to evaluate the limit. x²-2x-35 3. f(x) : x+5 -5.1 2.1 |-5.001 -5 -4.999 -4.99 -4.9 f(x) lim f(x) = %3D x--5

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Evaluating Limits by Creating a Table of Values**

To evaluate the limit of a function using a table of values, we follow this process:

**Problem:**

For the function \( f(x) = \frac{x^2 - 2x - 35}{x + 5} \), create your own table of values to evaluate the limit.

**Given Function:**

\[ f(x) = \frac{x^2 - 2x - 35}{x + 5} \]

**Steps:**

1. We choose several values of \( x \) around the point of interest (in this case, \( x = -5 \)).
2. Substitute these values into the function to get the corresponding \( f(x) \) values.
3. Analyze the behavior of \( f(x) \) as \( x \) approaches -5 from both the left and the right sides.

**Table of Values:**

\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & -5.1 & 2.1 & -5.001 & -5 & -4.999 & -4.99 & -4.9 \\
\hline
f(x) & & & & & & & \\
\hline
\end{array}
\]

**Limit Calculation:**

\[ \lim_{x \to -5} f(x) = \]

As \( x \) gets closer to -5 from the left (\( x \to -5^- \)) and from the right (\( x \to -5^+ \)), observe the values of \( f(x) \) to determine the limit. Fill in the table by calculating \( f(x) \) for each given \( x \) value.

This process helps us understand how \( f(x) \) behaves near \( x = -5 \) and determine its limit at that point.
Transcribed Image Text:**Evaluating Limits by Creating a Table of Values** To evaluate the limit of a function using a table of values, we follow this process: **Problem:** For the function \( f(x) = \frac{x^2 - 2x - 35}{x + 5} \), create your own table of values to evaluate the limit. **Given Function:** \[ f(x) = \frac{x^2 - 2x - 35}{x + 5} \] **Steps:** 1. We choose several values of \( x \) around the point of interest (in this case, \( x = -5 \)). 2. Substitute these values into the function to get the corresponding \( f(x) \) values. 3. Analyze the behavior of \( f(x) \) as \( x \) approaches -5 from both the left and the right sides. **Table of Values:** \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -5.1 & 2.1 & -5.001 & -5 & -4.999 & -4.99 & -4.9 \\ \hline f(x) & & & & & & & \\ \hline \end{array} \] **Limit Calculation:** \[ \lim_{x \to -5} f(x) = \] As \( x \) gets closer to -5 from the left (\( x \to -5^- \)) and from the right (\( x \to -5^+ \)), observe the values of \( f(x) \) to determine the limit. Fill in the table by calculating \( f(x) \) for each given \( x \) value. This process helps us understand how \( f(x) \) behaves near \( x = -5 \) and determine its limit at that point.
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