Question

evaluate limit as x approaches 1 at f of x for f of x equals the quantity 5 times x minus 11 for x less than 1, equals 1 for x equals 1 and equals negative 3 times x plus 6 for x greater than 1.

Answer 1

`\lim_(x \to 1) f(x)\\f(x)= \[\begin{cases}5x-11&x\ \textless \ 1\\ 1&x=1\\-3x+6&x\ \textgreater \ 1\end{cases}\] \\ \lim_(x \to 1^-) f(x)=5(1)-11=5-11=-6\\f(1)=1\\ \lim_(x \to 1^+) f(x)=-3(1)+6=-3+6=3`

Since,
`\lim_(x \to 1^-) f(x)\\eq\lim_(x \to 1^+) f(x)\\eq f(1)`
Therefore, the limit of f(x) as x tends to 1 does not exist.