g(x)=\frac{1}{2\sqrt{x}} g(25)=2 to advance in the circuit, locate g(8).

Question

Accepted Answer

# Explanation:
## Step1: Integrate $g'(x)$
We know that if $g'(x)=\frac{1}{2\sqrt{x}} = \frac{1}{2}x^{-\frac{1}{2}}$. Using the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$), then $\int g'(x)dx=\int\frac{1}{2}x^{-\frac{1}{2}}dx$.
$$
\begin{align*}
g(x)&=\frac{1}{2}\times\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C\
&=\frac{1}{2}\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C\
&=\sqrt{x}+C
\end{align*}
$$
## Step2: Find the value of $C$
Since $g(25) = 2$, substitute $x = 25$ into $g(x)=\sqrt{x}+C$.
$$
\begin{align*}
g(25)&=\sqrt{25}+C\
2&=5 + C\
C&=-3
\end{align*}
$$
## Step3: Calculate $g(8)$
Substitute $x = 8$ into $g(x)=\sqrt{x}-3$.
$$
g(8)=\sqrt{8}-3=2\sqrt{2}-3
$$

# Answer:
$2\sqrt{2}-3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Integrate \(g'(x)\)

Step2: Find the value of \(C\)

Step3: Calculate \(g(8)\)

Answer: