Solution:
we have been as asked to use properties of limits to find the indicated limit.
The given limit is
[tex] \lim_{x->0}(2x^2+2x+3)^2 [/tex]
The given limit can be evaluated as below
[tex] \lim_{x->0}(2x^2+2x+3)^2=(2*0^2+2*0+3)^2\\
\\
\lim_{x->0}(2x^2+2x+3)^2=(0+3)^2\\
\\
\lim_{x->0}(2x^2+2x+3)^2=3^2\\
\\
\lim_{x->0}(2x^2+2x+3)^2=9\\
[/tex]
Hence the correct option is A.
