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The handwritten answer to mathematical modeling was originally a computer exercise, and I hope to have an order.
1.( 1)

& gt& gt symbol x

& gt& gty = sin(3 * x)/(2 * x);

& gt& gt limit (y, x, 0)

ans =

3/2

(2)

& gt& gt symbol x

& gt& gty =(x^3+2*x^2- 1)/(2*x^2+3*x+ 1);

& gt& gt limit (y, x, inf)

ans =

Medium-range nuclear force

2.

& gt& gt symbol x

& gt& gty = 2+x^(3/2)-x;

& gt& gty 1 = diff(y,x)

y 1 =

(3*x^( 1/2))/2 - 1

& gt& gtsubs(y 1,x, 1)

ans =

0.5000

3.( 1)

& gt& gt symbol x

& gt& gty = log(x)/x;

& gt& gtint(y)

ans =

log(x)^2/2

(2)

& gt& gt symbol x

& gt& gty = exp(x)/( 1+exp(2 * x));

& gt& gtint(y,x,0, 1)

ans =

atan(exp( 1)) - pi/4

3.( 1)

& gt& gty = dsolve('Dy = y*sin(x)',' x ')

y =

C2/ exit (cos(x))

(2)

& gt& gty = dsolve('x*Dy+3*y=0 ',' y( 1)=2 ',' x ')

y =

2/x^3