What is the square root of 108 in simplest radical form.

Question

Marin Valencia · Accepted Answer

The right decision is A exists and equals 4.

f^{'} (x) = 7 - \frac{3}{4} * \frac{f (x)}{x}

...(1)
Let

y = f (x) ∴ f^{'} (x) = \frac{d y}{d x}

\Rightarrow \frac{d y}{d x} = 7 - \frac{3 y}{4 x}

\Rightarrow \frac{d y}{d x} + \frac{3 y}{4 x} = 7

An example of a linear differential equation is the one above

I . F . = e^{\int \frac{3}{4 x} d x} = x^{\frac{3}{4}}

\Rightarrow y * x^{\frac{3}{4}} = 7 \int x^{\frac{3}{4}} d x

\Rightarrow y * x^{\frac{3}{4}} = 4 x^{\frac{7}{4}} + c

\Rightarrow f (x) = 4 x + c * x^{- \frac{3}{4}}

Now,

lim_{x \to 0^{+}} x * f (\frac{1}{x}) = lim_{x \to 0^{+}} x (\frac{4}{x} + c x^{- \frac{3}{4}}) = 4

Answered question