Substitute x=2 into the expression inside the absolute value.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for problems 1, 2, 3, and 4.

1. Evaluate: $\lim_{x \to 2} |x - 2|$

Substitute $x=2$ into the expression inside the absolute value.
$x - 2 = 2 - 2 = 0$
Evaluate the absolute value of the result.
$|0| = 0$
The limit is $\boxed{\text{0}}$ .

2. Evaluate: $\lim_{x \to -3} |x + 3|$
Substitute $x=-3$ into the expression inside the absolute value.
$x + 3 = -3 + 3 = 0$
Evaluate the absolute value of the result.
$|0| = 0$
The limit is $\boxed{\text{0}}$ .

3. Evaluate: $\lim_{x \to 0} |x|$
Substitute $x=0$ into the expression inside the absolute value.
$x = 0$
Evaluate the absolute value of the result.
$|0| = 0$
The limit is $\boxed{\text{0}}$ .

4. Evaluate: $\lim_{x \to 5} |2x - 10|$
Substitute $x=5$ into the expression inside the absolute value.
$2x - 10 = 2(5) - 10 = 10 - 10 = 0$
Evaluate the absolute value of the result.
$|0| = 0$
The limit is $\boxed{\text{0}}$ .

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