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2. Let D =fxx(x,y)fyy(x,y) f2xy(x,y) IF (a) D > 0 AND fxx <0, f(x,y) is local max value (b) D > 0 AND fxx(x,y)>0 f(x,y) is local min value. 3. Determine if any boundary point gives min or max. Typically, we have to parametrize boundary and then reduce to a Calc 1 type of min/max problem to solve.
u~f(a;b;c) = ^urf(a;b;c) Tangent Planes let F(x,y,z) = k be a surface and P = (x 0;y 0;z 0) be a point on that surface. Equation of a Tangent Plane: rF(x 0;y 0;z 0)<x xx 0;y y 0;z z 0 > Approximations let z= f(x;y) be a di erentiable function total di erential of f = dz dz= rf<dx;dy> This is the approximate change in z The actual change in z is ...
This document contains a formula sheet for Calculus III with over 30 formulas covering topics like: - Vector operations including addition, dot and cross products - Cylindrical and spherical coordinate systems - Arc length, curvature, and osculating circles - Partial derivatives and differentials - Implicit and total differentiation - Linear ...
Here are a variety of ways to calculate distances using a mil-dot reticle. The first technique is especially useful because it enables you to base your calculation on
1. m= fa¢( ) is the slope of the tangent line to y= fx( ) at xa= and the equation of the tangent line at xa= is given by y=f(a)+-f¢(a)(xa). 2. fa¢( ) is the instantaneous rate of change of fx( ) at xa= . 3. If fx( ) is the position of an object at time x then fa¢( ) is the velocity of the object at xa= . Basic Properties and Formulas
This free Calculus 3 cheatsheet has a master list of common definitions, symbols, formulas, and notes, all in one place. Easily learn important topics with practice problems and flashcards, export your terms to pdf, and more.
ChemistryPrep.com 1 General Physics Equation Summary Sheet SI UNITS Length m Mass kg Time s Electric current A = ... 2nd Law F = ma 3rd Law F 1→2-F 2→1 Fg=G 1m2 r2 Gravity G=6.67×10−11 ... + ½ v 2 + gy ernoulli’s Equation GASES = F A Pressure p 1 V 1 = p 2 V 2 oyle’s Law V1 T1 = V2 T2 harles’ Law V1 n1 = V2 n2 Avogadro’s ...
