Problem with the function Limit in MATLAB

Hello, i'm having issues with the function Limit in MATLAB. I put this ecuation y = (x^2 - x - 2)*sqrt(a*x^2 + 1)/(x^2 - a); and then i tryed to do this function:

AHI = limit(y, x, -inf) but when I evaluated that, Matlab answered me with the same question, it answered me this: AHI =

limit(((a*x^2 + 1)^(1/2)*(- x^2 + x + 2))/(- x^2 + a), x, -Inf). Does anyone know what am I doing wrong or how can I solve it? Thank you.

but now I have another problem. With the same ecuation and now typing this, i get an error in another limit. What am I doing wrong in that one?

y = (x^2 - x - 2)*sqrt(a*x^2 + 1)/(x^2 - a);
assume(a, 'Real')
AVI = limit(y, x, a, 'left')
AVI =
((a^3 + 1)^(1/2)*(- a^2 + a + 2))/(- a^2 + a)

Answer 1

[Walter Roberson]

It is having trouble calculating the complex limit.

If you restrict a to real then it has no problem calculating the limit.

[Juan Rodríguez]

Thank you very much, but now I have another problem. With the same ecuation and now typing this, i get an error in another limit. What am I doing wrong in that one?

y = (x^2 - x - 2)*sqrt(a*x^2 + 1)/(x^2 - a);
assume(a, 'Real')
AVI = limit(y, x, a, 'left')
AVI =
((a^3 + 1)^(1/2)*(- a^2 + a + 2))/(- a^2 + a)

[Walter Roberson]

What error is that? That looks like a reasonable limit

[Juan Rodríguez]

My teacher used that function and this appeared:

y = x^2-9/x-a;
VIzq = limit(y, x, a, 'left')
piecewise(0 < a^2 - 9, -Inf, a^2 - 9 < 0, Inf, a == -3 | a == 3, 0)

[Walter Roberson]

That result is obviously wrong, unless a has been assigned something odd.

Consider for example a = 1, so a^2-9 = 1-9 = -8 which is < 0. According to the output shown, the limit should be Inf. So let us look:

x^2-9/x-1 as x approaches 1, does not involve a division by 0 and does not involve infinities. So the limit can be reached through plain substitution: (1)^2-9/1-1 -> 1-9-1 -> -9 . That is not even positive, let alone +infinity.

[Juan Rodríguez]

Okey, thank you very much