Question

Computer plot on the same axes several I_P(X) functions together with their common asymptotic approximation. Then computer plots each function with its small X approximation.

Short answer

The answer is given below.

Step-by-step solution

The concept of Wolfram Mathematica built-in functions

The Wolfram Mathematica built-in functions are used because they are very convenient. The Mathematica function Bessel returns the values of .

Use the wolfram Mathematica built-in function to plot the graphs 

The approximate formula for large X is, I_P(X)=$\frac{1}{\sqrt{2\mathrm{\pi X}}}{e}^X+O\left(\frac{e^X}{x}\right)$

The plot of the function I_P(X) together with its asymptotic approximate can be drawn as:

The approximate formula for small X is, I_P(X) = $\frac{1}{\neg (P+10}{\left(\frac{X}{2}\right)}^P+O\left(X^{P+2}\right)$.

The plot of the function I₀(X) together with its small 'X' approximate can be drawn as:

The plot of the function I_1/2(X) together with its small X approximate can be drawn as:

The plot of the function I₁(X) together with its small X approximate can be drawn as:

The plot of the function I_3/2(X) together with its small X approximate can be drawn as:

The plot of the function I₂(X) together with its small X approximate can be drawn as: