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$Question What number is marked by the dot on this number line? Enter your answer as a simplified improper fraction. If the fraction is negative, enter a negative numerator.$

Question $\newline$ What number is marked by the dot on this number line? $\newline$ Enter your answer as a simplified improper fraction. If the fraction is negative, enter a negative numerator.

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Find limits involving factorization and rationalization

Full solution

Q. Question

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What number is marked by the dot on this number line?

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Enter your answer as a simplified improper fraction. If the fraction is negative, enter a negative numerator.

Identify range and intervals: Identify the range and intervals on the number line. The number line starts at $0$ and ends at $2$ , with marks at every $\frac{1}{4}$ interval.
Determine dot position: Determine the exact position of the dot. The dot is located at the third mark after $1$ .
Calculate dot's value: Calculate the value of the dot's position. Since each interval represents $\frac{1}{4}$ , three intervals after $1$ is $1 + 3\left(\frac{1}{4}\right) = 1 + \frac{3}{4} = 1 \frac{3}{4}$ .
Convert to improper fraction: Convert the mixed number to an improper fraction. $1 \frac{3}{4}$ can be written as $(1\times\frac{4}{4}) + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}$ .

More problems from Find limits involving factorization and rationalization

Question

\lim _{x \rightarrow \infty} \frac{x^{2}-4}{x+4}

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1

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1

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-1

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0

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(D) The limit is unbounded

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Question

f(x)=\frac{6 x^{3}}{3 x+2}

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\lim _{x \rightarrow \infty} f(x)

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2

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3

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\newline

(D) The limit is unbounded

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\lim _{x \rightarrow 4} \frac{3 x}{(x-2)(x+2)}

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\newline

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(D) The limit doesn't exist

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Question

What is the average value of

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Question

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(A) It increases.

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(B) It decreases.

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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).

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