$\text{a)}$  

$\underset{x\to 1^{+}}{\lim }\sqrt{x-1}=\sqrt{1-1}=0$  

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$\text{b)}$  

$\underset{x\to -3^{+}}{\lim }\frac{3x+\sqrt{2x+6}}{x^2+1}=\frac{3\cdot \left(-3\right)+\sqrt{2\cdot \left(-3\right)+6}}{{\left(-3\right)}^2+1}=\frac{-9}{10}$  

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$\text{c)}$  

$\underset{x\to 4^{-}}{\lim }\left(\sqrt{4-x}+2x+3\right)=\sqrt{4-4}+2\cdot 4+3=11$  

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$\text{d)}$  

$\underset{x\to 2^{-}}{\lim }\frac{\sqrt{2-x}+7x+2}{x-4\sqrt{4-2x}}=\frac{\sqrt{2-2}+7\cdot 2+2}{2-4\sqrt{4-2\cdot 2}}=\frac{16}{2}=8$