Answer
(a) The given inequality does not provide sufficient information to determine $\lim _{x \rightarrow 1} f(x)$
(b) $\lim _{x \rightarrow 1} f(x)=1$
(c) $\lim _{x \rightarrow 1} f(x)=3$
Work Step by Step
(a) Because $\lim _{x \rightarrow 1}(4 x-5)=-1 \neq 1=\lim _{x \rightarrow 1} x^{2},$ the given inequality does not provide sufficient information to determine $\lim _{x \rightarrow 1} f(x)$
(b) Because $\lim _{x \rightarrow 1}(2 x-1)=1=\lim _{x \rightarrow 1} x^{2},$ it follows from the Squeeze Theorem that $\lim _{x \rightarrow 1} f(x)=1$
(c) Because $\lim _{x \rightarrow 1}\left(4 x-x^{2}\right)=3=\lim _{x \rightarrow 1}\left(x^{2}+2\right),$ it follows from the Squeeze Theorem that $\lim _{x \rightarrow 1} f(x)=3$
