find the limits. lim_x→2 (x - 7x + 1) edit view insert format tools table 12pt paragraph b i u a t²

Explanation:

Step1: Apply limit - sum rule

$\lim_{x\rightarrow2}(x^{2}-7x + 1)=\lim_{x\rightarrow2}x^{2}-\lim_{x\rightarrow2}7x+\lim_{x\rightarrow2}1$

Step2: Apply constant - multiple and constant rules

$\lim_{x\rightarrow2}x^{2}-7\lim_{x\rightarrow2}x+\lim_{x\rightarrow2}1$

Step3: Use direct - substitution

For $\lim_{x\rightarrow2}x^{2}$, substitute $x = 2$: $2^{2}=4$. For $\lim_{x\rightarrow2}x$, substitute $x = 2$: $2$. And $\lim_{x\rightarrow2}1=1$. So we have $4-7\times2 + 1$.

Step4: Calculate the result

$4-14 + 1=-9$

Answer:

$-9$