How to write equations ?

Hi,

I want to write this equation:

and also to to write the all element of that equation.

The equation is:

fullsimplify[series[sqrt(1+X), {x,0,3}]].

The element should be as:

1+x/2-x^2/8+x^3/16+O[x]^4/

Can someone guide how to write it in MATLAB code?

Thanks,

Ron

Answer 1

[Walter Roberson]

syms x
simplify(series(sqrt(1+x), x, 0, 'Order', 4))

[Ron Rivva]

Hi,

Thanks.

After applying your answer, an error occur:

>> equation
Error using sym/subsindex (line 769)
Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and
the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.

Error in sym/subsref (line 814)
            R_tilde = builtin('subsref',L_tilde,Idx);

Error in equation (line 2)
simplify(series(sqrt(1+x), x, 0, 'Order', 4))

Can you figure why ?

[Walter Roberson]

I suspect you had defined x as numeric not with the

syms x

that I showed.

>> syms x
simplify(series(sqrt(1+x), x, 0, 'Order', 4))
ans =
x^3/16 - x^2/8 + x/2 + 1

[Ron Rivva]

Hi, Thank you Walter for your response. Where do I need to define x ? in the line code? Can you guide how to write it ?

[Ron Rivva]

Got it.

Thanks Walter.

[Walter Roberson]

x is defined by

syms x

which is equivalent to

x = sym('x');

If you want to evaluate the expression with particular numeric versions of x, then use subs()

syms x
s = simplify(series(sqrt(1+x), x, 0, 'Order', 4));
xn = linspace(-10,10);
sn = double( subs(s, x, xn) );

Answer 2

[Image Analyst]

What does "O[]^4/" mean???

Anyway, start here:

for x = 0 : 3
  s(x+1) = 1+x/2-x^2/8+x^3/16
end
plot(s, 'b*-', 'LineWidth', 2);
grid on;
xlabel('x', 'FontSize', 20);
ylabel('s', 'FontSize', 20);

Adapt as needed. Like maybe after you have s, do

series = sqrt(1+s)

I didn't use X because we've already used lower case x and using both upper case X and lower case X would be confusing.

[Ron Rivva]

hi, I made a correction to my question. Can you check it again ?

Thanks

[Image Analyst]

OK, so now what does "O[x]^4/" mean? Is that zero times x to the fourth power divided by (some missing denominator)?

When you say "The element should be as:" do you mean that EACH element is that, so plus in 0 for x for the first term, plug in 1 for x for the second term, and so on? OR do you mean that that is is the first 5 terms, so 1 for was x=0, the second term is x/2 = 1/2 when x=1, and the third term is x^2/8 = 2^2/8 = 4/8 = 1/2 when x is 2, and so on?

Actually, can you just post a photo of the series because I'm not sure you can describe it unambiguously and I'd like to just see the standard mathematical notation?

[Walter Roberson]

The image that is shown in the original Question

is Mathematica code. The O[x]^4 is the Mathematica way of indicating that the series has been truncated at order 4 and that you need to add to the series some value that is proportional to x^4