APFIVE Evaluating a Limit Using Rationalization
Solve the equation: $$\lim_{x \to 1} \frac{\sqrt{x+3}-2}{x-1}$$.
| x | (sqrt(x+3)-2)/(x-1) |
|---|---|
| 0.9 | approx 0.25 |
| 1.1 | approx 0.25 |
A
After rationalizing the numerator by multiplying by the conjugate, the expression simplifies and evaluating at $$x = 1$$ gives $$\frac{1}{4}$$.
B
$$\frac{1}{2}$$
C
$$\frac{1}{\sqrt{x+3}+2}$$
D
$$\frac{1}{4}$$
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