User:A2569875/模板沙盒/數學測試/1

• 1.2247448713916+0.40824829046386i+0.40824829046386j+0.40824829046386k
• 1.2247448713916+0.40824829046386i+0.40824829046386j+0.40824829046386k, 1.5240983090117+0.32806282707854i+0.32806282707854j+0.32806282707854k, 1.7977905349536+0.27811916365045i+0.27811916365045j+0.27811916365045k, 2.0443701895132+0.24457410040745i+0.24457410040745j+0.24457410040745k, 2.2684248524173+0.22041726419422i+0.22041726419422j+0.22041726419422k, 2.4743684040981+0.2020717687681i+0.2020717687681j+0.2020717687681k, 2.665623993639+0.18757334162401i+0.18757334162401j+0.18757334162401k, 2.8447629753525+0.17576156760057i+0.17576156760057j+0.17576156760057k, 3.0137311915557+0.16590729836854i+0.16590729836854j+0.16590729836854k, 3.17402674572+0.15752860327161i+0.15752860327161j+0.15752860327161k,

八元數

• 1.2247448713916+0.40824829046386i+0.40824829046386j+0.40824829046386k
• 1.8243977430227+0.27406304459224i+0.27406304459224j+1.3703152229612k+0.54812608918448*il
• -k
• 4 sqrt=1.2247448713916+0.40824829046386i+0.40824829046386j+0.40824829046386k
• 8 sqrt=1.2247448713916+0.40824829046386i+0.40824829046386j+0.40824829046386k
• 4 sin=2.4525323488837+0.85399456491927i+0.85399456491927j+0.85399456491927k
• 8 sin=2.4525323488837+0.85399456491927i+0.85399456491927j+0.85399456491927k
• 4 cos=1.5747529115583-1.3300177322186i-1.3300177322186j-1.3300177322186k
• 8 cos=1.5747529115583-1.3300177322186i-1.3300177322186j-1.3300177322186k
• 4 sinh=-0.18868623578029+0.87934008360243i+0.87934008360243j+0.87934008360243k
• 8 sinh=-0.18868623578029+0.87934008360243i+0.87934008360243j+0.87934008360243k
• 4 asin=0.47445110698708+0.81968435336025i+0.81968435336025j+0.81968435336025k
• 8 asin=0.47445110698708+0.81968435336025i+0.81968435336025j+0.81968435336025k

M

• {{29,32,35,38},{65,72,79,86},{101,112,123,134}}
• ${{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {\begin{bmatrix}{7}&{8}&{9}&{10}\\{11}&{12}&{13}&{14}\end{bmatrix}}}={\begin{bmatrix}{29}&{32}&{35}&{38}\\{65}&{72}&{79}&{86}\\{101}&{112}&{123}&{134}\end{bmatrix}}$

??

解析失败 (语法错误): {\displaystyle { {{ {函數}:{{ {x}\mapsto{\left( { {{ {{ {4}\times {{ {x}^{2} }} }}-{{ {2}\times {x} }} }}+{1} }\right) } }} }};\,{函數 \left( 6\right) } } = 函數, 133 } ₁₂₃₄₅₆₇₈₉₀

極限與微分

精確度僅能到小數七位；太大的數字無法計算

極限

• $\lim _{{x}\to {0}^{+}}{\frac {x}{x}}=1$
• $\lim _{{x}\to {0}^{-}}{\frac {x}{x}}=1$
• $\lim _{{x}\to {0}^{}}{\frac {x}{x}}=1$
• $\lim _{{x}\to {0}^{+}}{\operatorname {sgn} x}=1$
• $\lim _{{x}\to {0}^{-}}{\operatorname {sgn} x}=-1$
• $\lim _{{x}\to {0}^{}}{\operatorname {sgn} x}=\mathrm {NaN}$
• 一般math：$\lim _{x\to 0^{}}{\frac {x}{x}}$
• $\left.{\frac {d\,{\cos x}}{d{x}}}\right|_{{x}={\frac {\pi }{6}}}=-0.49999999999587$
• 一般math：$\left.{\frac {d\cos(x)}{dx}}\right|_{x={\frac {\pi }{6}}}$

微分

• $\left.{\frac {d\,{{3}\,{{x}^{2}}}}{d{x}}}\right|_{{x}={2}}=12.000000000123$
• $\left.{\frac {d\,{cos}}{d{x}}}\right|_{{x}={\frac {{2}\,{\pi }}{3}}}=-0.86602540379001$
• $\left.{\frac {d\,{cos}}{d{x}}}\right|_{{x}={i}}=-7.4014868308344\times 10^{-12}-1.1752011936438i$
• $-{\sin {\frac {{2}\,{\pi }}{3}}}=-0.86602540378444$
• $\left.{\frac {d\,{\left\vert x\right\vert }}{d{x}}}\right|_{{x}={0}}=0$🤔
• $\left.{\frac {d\,{\left\vert x\right\vert }}{d{x}}}\right|_{{x}={1}}=1$
• $\left.{\frac {d\,{\left\vert x\right\vert }}{d{x}}}\right|_{{x}={-{1}}}=-1.000000000001$
• $\left.{\frac {d\,{\operatorname {sgn} x}}{d{x}}}\right|_{{x}={0}}=116666.66666667$ 囧rz……
• $\left.{\frac {d\,{\operatorname {sgn} x}}{d{x}}}\right|_{{x}={1}}=0$
• $\left.{\frac {d\,{\operatorname {sgn} x}}{d{x}}}\right|_{{x}={-{1}}}=0$

其他測試

• $\left.{\frac {d\,{\left.{\frac {d\,{cos}}{d{x}}}\right|_{{x}={x}}}}{d{x}}}\right|_{{x}={\frac {{2}\,{\pi }}{3}}}=0.49999989102378$（無法嵌套使用？）
• $\lim _{{x}\to {\frac {{2}\,{\pi }}{3}}^{}}{\left.{\frac {d\,{cos}}{d{x}}}\right|_{{x}={x}}}=-0.86602540378965$🤔🤔🤔🤔
• $\lim _{{x}\to {40}^{}}{5}=5$🤔
• $\left.{\frac {d\,{5}}{d{x}}}\right|_{{x}={40}}=0$🤔🤔

函數型運算子

• ${{{5}\cdot {7}}\cdot {9}}=315$

其他

• ${{\left(\sum _{{x}={1}}^{5}{{x}^{2}}\right)}-{5}}=50$
• $\mathrm {NaN} =\mathrm {NaN}$
• $\pi =3.1415926535898$
• $\infty =\infty$
• $sin=sin$
• ${{it}\mapsto {it}}=function1$
• ${{x}\mapsto {x}},{{x}\mapsto {\left({{x}^{2}}\right)}},{{x}\mapsto {\left({{x}^{3}}\right)}}=function1,function2,function3$🤔
• ${{f}:{{x}\mapsto {x}}}=f$
• ${{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}};\,{2}}=2$
• ${{sin};\,{2}}=2$
• cos
• ${{sin};\,{cos}}=cos$
• tan
• ${{{sin};\,{cos}};\,{tan}}=tan$
• sin, cos
• $sin,cos=sin,cos$
• 4.7177599838803
• ${{{sin};\,{cos}};\,{{{2}+{3}}-{{\sin 3}\times {2}}}}=4.7177599838803$
• ${{{sing};\,{2}};\,{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}}}=$
• ${{{f}:{{x}\mapsto {\left(x,\,{{x}+{1}}\right)}}};\,{f\left({{3}+{1}}\right)}}=5$

• ${{{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}};\,{{g}:{{x}\mapsto {\left({{f\left(x\right)}+{x}}\right)}}}};\,{f\left(3\right)}},g\left(3\right)=9,12$
• ${{{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}};\,{{g}:{{x}\mapsto {\left({{f\left(x\right)}+{x}}\right)}}}};\,{f\left(3\right)}},g\left(3\right),{{Minecraft}+{1}}=$

• ${{{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}};\,{{g}:{{x}\mapsto {\left({{f\left(x\right)}+{x}}\right)}}}};\,{f\left(3,\,4,\,5\right)}},g\left(3,\,4,\,5\right)=9,12$
• ${{{{f}:{{x}\mapsto {\left({{x}^{2}}\right)}}};\,{{g}:{{x}\mapsto {\left({{f\left(x\right)}+{x}}\right)}}}};\,{f\left(3,\,4,\,5\right)}},g\left(3,\,4,\,5\right),{{Minecraft}+{1}}=$

• ${{1}+{k}}=1+k$

• complex
• complex
• quaternion
• complex
• nan