Transcription of calc3 cheat sheet onesheet - Math
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calc3 cheat sheet onesheet - Math
DerivativesDxex=exDxsin(x)=cos(x)Dxcos(x )= sin(x)Dxtan(x)=sec2(x)Dxcot(x)= csc2(x)Dxsec(x)=sec(x)tan(x)Dxcsc(x)= csc(x)cot(x)Dxsin 1=1p1 x2,x2[ 1,1]Dxcos 1= 1p1 x2,x2[ 1,1]Dxtan 1=11+x2, 2 x 2 Dxsec 1=1|x|px2 1,|x|>1 Dxsinh(x)=cosh(x)Dxcosh(x)=sinh(x)Dxtanh (x)=sech2(x)Dxcoth(x)= csch2(x)Dxsech(x)= sech(x)tanh(x)Dxcsch(x)= csch(x)coth(x)Dxsinh 1=1px2+1 Dxcosh 1= 1px2 1,x >1 Dxtanh 1=11 x2 1<x<1 Dxsech 1=1xp1 x2,0<x<1 Dxln(x)=1xIntegralsR1xdx= ln|x|+cRexdx=ex+cRaxdx=1lnaax+cReaxdx=1a eax+cR1p1 x2dx= sin 1(x)+cR11+x2dx= tan 1(x)+cR1xpx2 1dx=sec 1(x)+cRsinh(x)dx= cosh(x)+cRcosh(x)dx= sinh(x)+cRtanh(x)dx= ln|cosh(x)|+cRtanh(x)sech(x)dx= sech(x)+cRsech2(x)dx= tanh(x)+cRcsch(x)coth(x)dx= csch(x)+cRtan(x)dx= ln|cos(x)|+cRcot(x)dx= ln|sin(x)|+cRcos(x)dx= sin(x)+cRsin(x)dx= cos(x)+cR1pa2 u2dx= sin 1(ua)+cR1a2+u2dx=1atan 1ua+cRln(x)dx=(xln(x)) x+cU-SubstitutionLetu=f(x)(canbemorethan onevariable).
Hyperboloid of One Sheet x2 a2 + y 2 b2 z2 c2 =1 Hyperboloid of Two Sheets z2 c2 x 2 a2 y b2 =1 (Major Axis: Z because it is the one not subtracted) Elliptic Paraboloid z= x 2 a 2 + y 2 b (Major Axis: z because it is the variable NOT squared) (Major Axis: Z axis because it is not squared) z= y 2 b2 x a2 Elliptic Cone (Major Axis: Z axis because ...
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