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Math 1501: Midterm Formula sheetby Dr. Patcharin T. Marion(Note: This sheet may have some formulas that you will not need.)Slope of the line passing through(x1; y1)and(x2; y2) =)m=y2°y1x2°x1wherex26=x1Equations of straight lines:Point-Slope FormSlope-Intercept Formy=m(x°x1) +y1y=mx+bwherem=slope,(x1; y1) =point on linewherem=slope,b=y-interceptVertical LineHorizontal Linex=ay=bQuadratic formula: Forax2+bx+c= 0, the value ofxis given byx=°b±pb2°4ac2a:Special Factoring:a3°b3= (a°b)°a2+ab+b2±Di/erence of Cubesa3+b3= (a+b)°a2°ab+b2±Sum of CubesSpecial limit:limx!0sinxx= 1andlimx!01°cosxx= 0:De°nition of the derivative of a function:f0(x) = limh!0f(x+h)°f(x)hAlternative form of derivative:f
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Unformatted text preview: d dx ( c ) = 0 d dx ( x n ) = nx n & 1 d dx (sin x ) = cos x d dx (csc x ) = & csc x cot x d dx (cos x ) = & sin x d dx (sec x ) = sec x tan x d dx (tan x ) = sec 2 x d dx (cot x ) = & csc 2 x d dx ( e x ) = e x d dx ( a x ) = (ln a ) a x d dx (ln x ) = 1 x d dx (log a x ) = 1 (ln a ) x ( fg ) = f g + fg ² f g ³ = f g & fg g 2 d dx ( f ( g ( x ))) = f ( g ( x )) ² g ( x ) Some geometry formulas: Shape Surface Area Volume cube SA = 6 x 2 V = x 3 sphere SA = 4 &r 2 V = 4 3 &r 3...
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