Factor[3x^2-5x-2]

Factor[2x^2-9x+10]

Limit[(3x^2-5x-2)/(2x^2-9x+10),x->2]

Limit[(Sqrt[1-x]-1)/x,x->0]

Integrate[1/(1+x^2),{x,1,Infinity}]

Integrate[1/(x^2),{x,1,Infinity}]

Integrate[1/Sqrt[1-x^2],{x,0,1}]

Plot[1/Sqrt[1-x^2],{x,-1,1}]

Table[1/Sqrt[1-x^2],{x,0,1,1/25}]

1/Sqrt[1-x^2]/.x->{3/5,4/5,24/25}

(5/4)(1/5)+(4/5)(24/25-4/5)+(25/7)(1/25)

N[%]

N[Sqrt[3]/2]

Sqrt[1-x^2]/.x->{7/25,3/5,4/5,Sqrt[3]/2,24/25}

Plot[{Sqrt[1-x^2],1-x/3,7/5-x,3-3x},{x,0,1},PlotRange->{0,1},AspectRatio->1,PlotStyle->{Thickness[0.01],Thickness[0.002],Thickness[0.002],Thickness[0.002]}]

Integrate[1-x/3,{x,0,3/5}]+Integrate[7/5-x,{x,3/5,4/5}]+Integrate[3-3x,{x,4/5,1}]

4%

N[%]

Plot[{Sqrt[1-x^2],1-1/7 x,11/10-1/2x,7/5-x,11/5-2x,7-7x},{x,0,1},PlotRange->{0,1},AspectRatio->1]

Integrate[1-x/7,{x,0,7/25}]+Integrate[11/10-x/2,{x,7/25,3/5}]+Integrate[7/5-x,{x,3/5,4/5}]+Integrate[11/5-2x,{x,4/5,24/25}]+Integrate[7-7x,{x,24/25,1}]

%*4

3*125

N[%]

N[%]

4*%

Solve[{a (0)+b==1,a(7/25)+b==24/25},{a,b}]

Solve[{a (3/5)+b==4/5,a(7/25)+b==24/25},{a,b}]

Solve[{a (4/5)+b==3/5,a(24/25)+b==7/25},{a,b}]

Solve[{a (1)+b==0,a(24/25)+b==7/25},{a,b}]

Integrate[1-x/3,{x,0,3/5}]+Integrate[7/5-2x,{x,3/5,4/5}]+Integrate[3-3x,{x,4/5,1}]

4*N[%]

4*%

(4/5)(3/5-0)+(3/5)(4/5-3/5)+(1/2)(Sqrt[3]/2-4/5)+(7/25)(24/25-Sqrt[3]/2)

4N[%]

Graphics[
{Thick,
Circle[{0,0},1,{0,Pi/2}],
Line[{{0,0},{0,1}}],
Line[{{0,0},{1,0}}],
Opacity[0.5],Pink,EdgeForm[{Thickness[0.003],Black}],
Polygon[{{0,0},{0,1},{3/5,4/5},{4/5,3/5},{1,0}}],
Black,PointSize[0.04],Opacity[1],
Point[{ 
{0,1},{3/5,4/5},{4/5,3/5},{1,0}
}]
}]

Graphics[
{Thick,
Circle[{0,0},1,{0,Pi/2}],
Line[{{0,0},{0,1}}],
Line[{{0,0},{1,0}}],
Opacity[0.5],Pink,EdgeForm[{Thickness[0.003],Black}],
Polygon[{{0,0},{0,1},{7/25,24/25},{3/5,4/5},{4/5,3/5},{24/25,7/25},{1,0}}],
Black,PointSize[0.04],Opacity[1],
Point[{ 
{0,1},{7/25,24/25},{3/5,4/5},{4/5,3/5},{24/25,7/25},{1,0}
}]
}]

Graphics[
{
Opacity[0.3],
Green,EdgeForm[{Thickness[0.003],Black}],
Polygon[{{1,1},{-1,1},{-1,-1},{1,-1}}],
Blue,Polygon[{{1,0},{0,1},{-1,0},{0,-1}}],
Thick,Opacity[1],Black,Circle[{0,0},1]
}]

1-(24/25)^2

Solve[x^2-3x+2==0]

Plot[Cos[x/2],{x,0,Pi}]

Cos[2x]

Plot[10/(x-2),{x,1,3}]

10/(x-2)/.x->{1,3}

Integrate[x^2,{x,0,1}]

Solve[2x^3==1/2]

Plot[{x^2,1/Sqrt[3]},{x,0,1}]

Limit[(Cos[Pi/3+h]-1/2)/h,h->0]

(x^2-x-2)(x-2)/( Sqrt[16+x^2])/.x->-2.0

Plot[(x^2-x-2)(x-2)/( Sqrt[16+x^2]),{x,-2,3},PlotRange->{-3,1.5}]

D[(x-2)/Sqrt[1+x^2],x]

Plot[%,{x,-3,3}]

Plot[NIntegrate[(x^2-x-2)(x-2)/( Sqrt[16+x^2]),{x,0,t}],{t,-2,3}]

Plot[NIntegrate[(x-1)/Sqrt[1+x^2],{x,-1,t}],{t,-1,3}]

Table[1/Sqrt[1-x^2],{x,-1,1,1/50}]

Limit[x( Sqrt[1+1/x]-1),x->Infinity]

Plot[Cos[Sqrt[t]],{t,0,4Pi^2},Ticks->{{Pi^2/4,Pi^2,9/4Pi^2,4Pi^2},{-1,1}}]

Integrate[Cos[Sqrt[t]],t]

(%/.(t->9/4Pi^2))

Plot[2 Cos[(Sqrt[t])]+2 (Sqrt[t]) Sin[(Sqrt[t])],{t,0,4 Pi^2},Ticks->{{Pi^2/4,Pi^2,9/4Pi^2,4Pi^2},{-3Pi, -2Pi, -Pi, Pi, 2Pi, 3Pi}}]

N[Pi^2]

N[Pi^2/2]

55+89

Integrate[1/Sqrt[x],{x,0,1}]

Plot[Floor[(x-2)(x-1)],{x,1,5}]