if lim h(x) = 12, what is the value of lim x - h(x)? x→-5 x→-5

Answer:

-17

Explanation:

Step1: Apply limit - difference rule

$\lim_{x\rightarrow - 5}[x - h(x)]=\lim_{x\rightarrow - 5}x-\lim_{x\rightarrow - 5}h(x)$

Step2: Find $\lim_{x\rightarrow - 5}x$

$\lim_{x\rightarrow - 5}x=-5$

Step3: Substitute known values

Since $\lim_{x\rightarrow - 5}h(x) = 12$, then $\lim_{x\rightarrow - 5}x-\lim_{x\rightarrow - 5}h(x)=-5 - 12=-17$