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This section is usually the first quarter of the module. You need to know if a series converges or diverges instantly. Standard formulas for Sncap S sub n S∞cap S sub infinity end-sub Convergence Tests: Divergence Test: If , it diverges. Ratio Test: Essential for power series ( converges). Integral Test & P-series: Remember that converges if

Partial derivatives, Chain Rule for multiple variables, Gradient vectors, and Directional derivatives. ma1511 cheat sheet

Cylindrical: [ x = r\cos\theta,\ y = r\sin\theta,\ z = z,\ dV = r , dz , dr , d\theta ] This section is usually the first quarter of the module

: [ x = \rho\sin\phi\cos\theta,\ y = \rho\sin\phi\sin\theta,\ z = \rho\cos\phi, ] [ dV = \rho^2 \sin\phi, d\rho, d\phi, d\theta. ] Ratio Test: Essential for power series ( converges)

( ( f(-x)=f(x) ) ): ( b_n = 0 ), only cosine terms remain.

Let ( D = f_xxf_yy - (f_xy)^2 ):