12-16-2019, 03:02 PM
Nonsense, paste code
xcas get
mathematica also calculated for a long time
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)
hp prime get
We find f (0) = 0 and substitute it into the result,Get the limit
hp prime get
This is the correct answer
Code:
limit((∫(∫(sin(t)*atan(1+t),t,0,u^2),u,0,x))/(x^3*((x+1)^(1/3)-1)^2),x,0)
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)))
Code:
9*π/40