Question

X² + 8x + 17, x ≤ -5X+4,x>-52B) Does not exist.5) lim f(x), f(x) =x->-5

Answer 1

`\begin{gathered} \lim_(x\to-5)f(x) \\ \\ f(x)=\begin{cases}x^2+8x+17,x\leq-5{} \\ -(x)/(2)+4,x>-5{}\end{cases} \end{gathered}`

Evaluate each limit separately:

`\begin{gathered} \lim_(x\to-5)x^2+8x+17 \\ \\ \lim_(x\to-5)(-5)^2+8(-5)+17=25-40+17=2 \\ \\ \end{gathered}`
`\begin{gathered} \lim_(x\to-5)-(x)/(2)+4 \\ \\ \lim_(x\to-5)-(-5)/(2)+4=(5)/(2)+4=(5+8)/(2)=(13)/(2)=6.5 \end{gathered}`

As the one-sides limits are different, the limit doesn't exist

Answer: Does not exist.