Find the following limits:
(a) Find lim x → 2 g ( x ) , {\displaystyle \lim _{x\rightarrow 2}g(x),} provided that lim x → 2 [ 4 − g ( x ) x ] = 5. {\displaystyle \lim _{x\rightarrow 2}{\bigg [}{\frac {4-g(x)}{x}}{\bigg ]}=5.}
(b) Find lim x → 0 sin ( 4 x ) 5 x {\displaystyle \lim _{x\rightarrow 0}{\frac {\sin(4x)}{5x}}}
(c) Evaluate lim x → − 3 + x x 2 − 9 {\displaystyle \lim _{x\rightarrow -3^{+}}{\frac {x}{x^{2}-9}}}
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provided that ![{\displaystyle \lim _{x\rightarrow 2}{\bigg [}{\frac {4-g(x)}{x}}{\bigg ]}=5.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81d23dbe64c4cb46da5b3a09f0267a3cfbe494f1)
