[Discussion] Solving the Limit Problem - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: [Discussion] Solving the Limit Problem (/thread-14181.html) [Discussion] Solving the Limit Problem - yangyongkang - 12-16-2019 03:02 PM 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` This is the correct answer RE: [Discussion] Solving the Limit Problem - yangyongkang - 12-19-2019 09:08 AM Several perverted integrals (i) Code: `evalf(int(1/(1+e^(1/x)),x,-1,1))` The answer is 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)` The answer is Code: `x+x*tan(x)` (iii) Code: `simplify(int((x*tan(x)+ln(x*cos(x))-1)/ln(x*cos(x))^2,x))` The answer is Code: `x/ln(x*ln(x))`