$\lim_{x \rightarrow 0} \left(\frac{ 2{x}^{2}-3x+4+5x-4 }{ x }\right)$
Since evaluating limits of the numerator and denominator would result in an indeterminate form, use the L'Hopital's rule$\lim_{x \rightarrow 0} \left(\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{2}-3x+4+5x-4 \right) }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( x \right) }\right)$
Find the derivative$\lim_{x \rightarrow 0} \left(\frac{ 4x+2 }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( x \right) }\right)$
Find the derivative$\lim_{x \rightarrow 0} \left(\frac{ 4x+2 }{ 1 }\right)$
Any expression divided by $1$ remains the same$\lim_{x \rightarrow 0} \left(4x+2\right)$
Evaluate the limit$4 \times 0+2$
Simplify the expression$2$