Midterm 2-Formula Sheet

Midterm 2-Formula Sheet - + = dt dt dy dt dx L 2 2 Polar...

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Formula Sheet for Midterm 2 Derivatives: 2 1 1 1 ) (sin x x dx d = 1 | | 1 ) (csc 2 1 = x x x dx d 2 1 1 1 ) (tan x x dx d + = Integrals: + = + C a x a dx a x 1 2 2 tan 1 1 C x x xdx + + = | tan sec | ln sec C x x xdx + = | cot csc | ln csc + = C x xdx | sec | ln tan + = C x xdx | sin | ln cot Trig Identities: () ) 2 cos( 1 2 1 ) ( sin 2 x x = () ) 2 cos( 1 2 1 ) ( cos 2 x x + = x x x cos sin 2 2 sin = x x x 2 2 sin cos 2 cos = x 2 sin 2 1 = 1 cos 2 2 = x Miscellaneous Formulas: Arc length: + = b a dx dx dy L 2 1 Surface Area (of Revolution): + = b a dx dx dy y S 2 1 2 π Work: = b a dx x f W ) ( Volume (of Revolution): = b a dx x A V ) ( Hydrostatic Force on dam: = b a dy y w y d g F ) ( ) ( ρ Cardiac Output: = T dt t c A F 0 ) ( Mean for a probability density function: = dx x xf ) ( μ Exponential Density Function: 0 , 1 ) ( = t e t f t Euler’s Method: ) , ( 1 1 1 + = n n n n y x hF y y Parametric Arc length:
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Unformatted text preview: + = dt dt dy dt dx L 2 2 Polar Curves Arc length: + = b a d d dr r L 2 2 Polar Curves Area: = b a d r A 2 2 1 NOTE: In addition, the formulas for the second derivative of a curve given by parametric equations and Newtons law of Cooling will be provided, if required, within the question. Any other formulas that were provided for the 1 st midterms will also be provided, if needed, within the question....
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