[Discussion] Solving the Limit Problem
12-16-2019, 03:02 PM
Post: #1
 yangyongkang Junior Member Posts: 47 Joined: Dec 2018
[Discussion] Solving the Limit Problem
Nonsense, paste code
Code:
limit((∫(∫(sin(t)*atan(1+t),t,0,u^2),u,0,x))/(x^3*((x+1)^(1/3)-1)^2),x,0)
xcas get
Code:
"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"

mathematica also calculated for a long time
Code:
Limit[Integrate[Sin[t]*ArcTan[1 + t], {u, 0, x}, {t, 0, u^2}]/(  x^3*((x + 1)^(1/3) - 1)^2), x -> 0]

Surprisingly, the Ti Nspire CX CII CAS is calculated

In fact, the hp prime can be calculated, and it needs to be replaced by another method.

let f(t)=sin(t)*atan(1+t)

Code:
series((∫(∫(f(t),t,0,u^2),u,0,x)/(x^3*((x+1)^(1/3)-1)^2)),equal(x,0),1)

hp prime get
Code:
(3*f(0)/x^2)+(2*f(0)/x)+(9/10)*(function_diff(f))(0)-(1/9)*f(0)+((3/5)*(function_diff(f))(0)+(2/27)*f(0))*x+x^2*order_size(x)

We find f (0) = 0 and substitute it into the result,Get the limit
Code:
((9/10)*∂(sin(t)*atan(1+t),t)|(equal(t,0)))
hp prime get
Code:
9*π/40

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12-19-2019, 09:08 AM
Post: #2
 yangyongkang Junior Member Posts: 47 Joined: Dec 2018
RE: [Discussion] Solving the Limit Problem
Several perverted integrals
(i)
Code:
evalf(int(1/(1+e^(1/x)),x,-1,1))
xcas get
Code:
"Unidirectional limits are distincts 1,0 Error: Bad Argument Valu"

(ii)
Code:
int(x^2*tan(x)^2+x^2+2*x*tan(x)+1,x)
Code:
x+x*tan(x)

(iii)
Code:
simplify(int((x*tan(x)+ln(x*cos(x))-1)/ln(x*cos(x))^2,x))
x/ln(x*ln(x))