if lim k(x) = -10, what is the value of lim x - k(x)? x→ - 5 x→ - 5

Answer:

15

Explanation:

Step1: Use limit - difference rule

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

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

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

Step3: Substitute known values

Since $\lim_{x\rightarrow - 5}k(x)=-10$, then $\lim_{x\rightarrow - 5}x-\lim_{x\rightarrow - 5}k(x)=-5-(-10)$

Step4: Simplify the expression

$-5 - (-10)=-5 + 10=15$