Question

Help please! Worth some points!

Answer 1

`f(x)=\begin{cases}5-x^2&\text{for }x<0\\-5&\text{for }x=0\\2x+5&\text{for }x>0\end{cases}`


`\displaystyle\lim_(x\to0^-)f(x)=\lim_(x\to0)(5-x^2)=5`

`\displaystyle\lim_(x\to0^+)f(x)=\lim_(x\to0)(2x+5)=5`

`\implies\displaystyle\lim_(x\to0)f(x)=5`

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`f(x)=\begin{cases}x-3&\text{for }x<4\\x+3&\text{for }x>4\end{cases}`


`\displaystyle\lim_(x\to4^-)f(x)=\lim_(x\to4)(x-3)=1`

`\displaystyle\lim_(x\to4^+)f(x)=\lim_(x\to4)(x+3)=7`

`\implies\displaystyle\lim_(x\to4)f(x)\text{ does not exist}`