Evaluating Limits

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GRE Quantitative Reasoning › Evaluating Limits

Questions 1 - 1

Evaluate: $\lim_{x \to 2} \frac {x-2}{x^2-4}$

$\frac {1}{4}$

$-\frac {1}{4}$

Undefined/No Limit

$\frac {1}{2}$

Step 1: See if we can plug in into the equation..

We can't because the denominator becomes ..

Step 2: Factor the denominator:

(By the Difference of Perfect Squares Formula)

Step 3: Re-write the function:

$\frac {(x-2)}{[(x-2)(x+2)]}$

Step 4: Divide by on both the numerator and denominator because it's common:

We are left with: $\frac {1}{(x+2)}$

Step 5: Plug in :

$\frac {1}{2+2}\implies \frac {1}{4}$

The limit of this function as x approaches 2 is $\frac {1}{4}$ .