Find the limit $\lim _{x \rightarrow 2} \frac{x-1}{x^{2}-4 x+7}$ .
A) $\frac{1}{7}$
B) $\frac{1}{3}$
C) $-1$
D) 1

Question

Quizplus · Accepted Answer

We can try to directly substitute $x=2$ in the expression, but we get an indeterminate form $\frac{0}{3}$. Therefore, we can try factoring the denominator to simplify the expression:
$$x^2-4x+7=(x-2)^2+3$$
Substituting this in the expression, we get:
$$\lim_{x\rightarrow 2}\frac{x-1}{(x-2)^2+3}$$
Now, substituting $x=2$ directly gives the answer $\frac{1}{3}$. Therefore, the limit evaluated at $x=2$ is $\frac{1}{3}$, and hence the answer is B.

Find the Limit lim⁡x→2x−1x2−4x+7\lim _{x \rightarrow 2} \frac{x-1}{x^{2}-4 x+7}limx→2​x2−4x+7x−1​ A) 17\frac{1}{7}71​

Find the Limit $\lim _{x \rightarrow 2} \frac{x-1}{x^{2}-4 x+7}$
A) $\frac{1}{7}$