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Wize High School Grade 12 Calculus Textbook > Rate of Change

Evaluating 00\frac{0}{0} Limits -- by Factoring

Limits of the Form 00\frac{0}{0}Previous Section
Evaluating 00\frac{0}{0} Limits -- with RadicalsNext Section
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Example: Factoring 0/0 Limits

Evaluate lim⁡x→2 x2−4x−2\displaystyle\lim_{x\to2}\ \frac{x^2-4}{x-2}.

Direct substituteion gives us 00\frac{0}{0}, try factoring:

lim⁡x→2(x+2)(x−2)x−2\displaystyle\lim_{x\rightarrow2}\frac{\left(x+2\right)\left(x-2\right)}{x-2}
=lim⁡x→2x+2\displaystyle=\lim_{x\rightarrow2}x+2
=4=4

Practice: Factoring 0/0 Limits

lim⁡h→0 4−(5h+2)2h=\displaystyle\lim_{h\to0}\ \frac{4-\left(5h+2\right)^2}{h}=

Practice: 0/0 Limit

Evaluate lim⁡t→1 3t−31−t\displaystyle\lim_{t\to1}\ \frac{\frac{3}{t}-3}{1-t}, if it exists.