Question

plz solve this... ......
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Answer 1

$\displaystyle\\\lim_{x\to 0}\dfrac{\sqrt{4+5x}-2}{x}=\\\\\lim_{x\to 0}\dfrac{(\sqrt{4+5x}-2)(\sqrt{4+5x}+2)}{x(\sqrt{4+5x}+2)}=\\\\\lim_{x\to 0}\dfrac{4+5x-4}{x(\sqrt{4+5x}+2)}=\\\\\lim_{x\to 0}\dfrac{5x}{x(\sqrt{4+5x}+2)}=\\\\\lim_{x\to 0}\dfrac{5}{\sqrt{4+5x}+2}=\\\\\dfrac{5}{\sqrt{4+5\cdot 0}+2}=\dfrac{5}{2+2}=\dfrac{5}{4}$