QuestionGiven the table of $x$ and $f(x)$ values, which limit conclusion about $f(x)$ as $x$ approaches 6 is correct? (A) $\lim _{x \rightarrow 6} f(x)=0$ (B) $\lim _{x \rightarrow 6} f(x)=6$ (C) $\lim _{x \rightarrow 6} f(x)=10$ (D) $\lim _{x \rightarrow 6} f(x)$ does not exist.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is given at selected values of $x$ . . We are interested in the limit of $f(x)$ as $x$ approaches6.

STEP 2

To find the limit of a function as $x$ approaches a certain value, we need to look at the behavior of the function as $x$ approaches that value from both the left and the right.

STEP 3

First, let's look at the behavior of $f(x)$ as $x$ approaches6 from the left. This means we look at the values of $f(x)$ for $x$ slightly less than6.

STEP 4

Looking at the table, as $x$ approaches6 from the left (i.e., $x$ =.999), $f(x)$ appears to be increasing without bound.

STEP 5

Now, let's look at the behavior of $f(x)$ as $x$ approaches from the right. This means we look at the values of $f(x)$ for $x$ slightly more than.

STEP 6

Looking at the table, as $x$ approaches6 from the right (i.e., $x$ =6.001), $f(x)$ appears to be decreasing without bound.

STEP 7

The limit of a function as $x$ approaches a certain value exists only if the function approaches the same value from both the left and the right.

STEP 8

However, in this case, as $x$ approaches6, $f(x)$ is increasing without bound from the left and decreasing without bound from the right.

STEP 9

Therefore, the limit of $f(x)$ as $x$ approaches6 does not exist.
So, the correct answer is () $\lim{x \rightarrow6} f(x)$ does not exist.

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QuestionGiven the table of $x$ and $f(x)$ values, which limit conclusion about $f(x)$ as $x$ approaches 6 is correct? (A) $\lim _{x \rightarrow 6} f(x)=0$ (B) $\lim _{x \rightarrow 6} f(x)=6$ (C) $\lim _{x \rightarrow 6} f(x)=10$ (D) $\lim _{x \rightarrow 6} f(x)$ does not exist.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is given at selected values of $x$ . . We are interested in the limit of $f(x)$ as $x$ approaches6.

STEP 2

To find the limit of a function as $x$ approaches a certain value, we need to look at the behavior of the function as $x$ approaches that value from both the left and the right.

STEP 3

First, let's look at the behavior of $f(x)$ as $x$ approaches6 from the left. This means we look at the values of $f(x)$ for $x$ slightly less than6.

STEP 4

Looking at the table, as $x$ approaches6 from the left (i.e., $x$ =.999), $f(x)$ appears to be increasing without bound.

STEP 5

Now, let's look at the behavior of $f(x)$ as $x$ approaches from the right. This means we look at the values of $f(x)$ for $x$ slightly more than.

STEP 6

Looking at the table, as $x$ approaches6 from the right (i.e., $x$ =6.001), $f(x)$ appears to be decreasing without bound.

STEP 7

The limit of a function as $x$ approaches a certain value exists only if the function approaches the same value from both the left and the right.

STEP 8

However, in this case, as $x$ approaches6, $f(x)$ is increasing without bound from the left and decreasing without bound from the right.

STEP 9

Therefore, the limit of $f(x)$ as $x$ approaches6 does not exist.
So, the correct answer is () $\lim{x \rightarrow6} f(x)$ does not exist.

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Studdy Solution

STEP 1

Assumptions1. The function fff is given at selected values of xxx. . We are interested in the limit of f(x)f(x)f(x) as xxx approaches6.

STEP 2

To find the limit of a function as xxx approaches a certain value, we need to look at the behavior of the function as xxx approaches that value from both the left and the right.

STEP 3

First, let's look at the behavior of f(x)f(x)f(x) as xxx approaches6 from the left. This means we look at the values of f(x)f(x)f(x) for xxx slightly less than6.

STEP 4

Looking at the table, as xxx approaches6 from the left (i.e., xxx =.999), f(x)f(x)f(x) appears to be increasing without bound.

STEP 5

Now, let's look at the behavior of f(x)f(x)f(x) as xxx approaches from the right. This means we look at the values of f(x)f(x)f(x) for xxx slightly more than.

STEP 6

Looking at the table, as xxx approaches6 from the right (i.e., xxx =6.001), f(x)f(x)f(x) appears to be decreasing without bound.

STEP 7

The limit of a function as xxx approaches a certain value exists only if the function approaches the same value from both the left and the right.

STEP 8

However, in this case, as xxx approaches6, f(x)f(x)f(x) is increasing without bound from the left and decreasing without bound from the right.

STEP 9

Therefore, the limit of f(x)f(x)f(x) as xxx approaches6 does not exist.So, the correct answer is () lim⁡x→6f(x)\lim{x \rightarrow6} f(x)limx→6f(x) does not exist.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The function $f$ is given at selected values of $x$ . . We are interested in the limit of $f(x)$ as $x$ approaches6.

To find the limit of a function as $x$ approaches a certain value, we need to look at the behavior of the function as $x$ approaches that value from both the left and the right.

First, let's look at the behavior of $f(x)$ as $x$ approaches6 from the left. This means we look at the values of $f(x)$ for $x$ slightly less than6.

Looking at the table, as $x$ approaches6 from the left (i.e., $x$ =.999), $f(x)$ appears to be increasing without bound.

Now, let's look at the behavior of $f(x)$ as $x$ approaches from the right. This means we look at the values of $f(x)$ for $x$ slightly more than.

Looking at the table, as $x$ approaches6 from the right (i.e., $x$ =6.001), $f(x)$ appears to be decreasing without bound.

The limit of a function as $x$ approaches a certain value exists only if the function approaches the same value from both the left and the right.

However, in this case, as $x$ approaches6, $f(x)$ is increasing without bound from the left and decreasing without bound from the right.

Therefore, the limit of $f(x)$ as $x$ approaches6 does not exist.
So, the correct answer is () $\lim{x \rightarrow6} f(x)$ does not exist.