Question

Find (in terms of the constant a)

\lim_{h\rightarrow 0} \frac{\sqrt{3(a+h)} - \sqrt{3 a}}{h}.
can someone show me step by step how to solve this?

Answer 1

@jim_thompson5910 can you help me? :)

Answer 2

? that came up blank

Answer 3

Since h->0, \[\frac{h}{a}<<1\]so according to Binomial theorem\[(1+\frac{h}{a})^{\frac{1}{2}}=(1+\frac{1}{2}\times \frac{h}{a})\]Plug this into the original expression