Question

Are b and c the is thing?

Answer 1

A)
`f` is continuous at
`x=1`

Explanation:

Compute the left and right side limits of f(x) as x approaches 1

`\displaystyle \lim_(x \to 1^-) f(x)=2^1=2\\\\\lim_(x \to 1^+)f(x)=(1)/(2)(1)^2-1+(5)/(2)=2`

Since
`\displaystyle \lim_(x \to 1^-) f(x)= \lim_(x \to 1^+) f(x)`, then
`\displaystyle \lim_(x \to 1) f(x)` exists, which makes A true.