CAP Cheat Sheet

The exam allows us to bring in 3 A4 pages. In them, there will be:

• Riemann Sums

  • Definition
  • Area under curve
  • Left and Right

• Limit Laws

• Obviously all calculus laws

  • Integrals and Differentiations
    • Plus reminder to include ends when doing u-sub with definite integrals
  • Including Fundamental Theorem of Calculus
  • Chain Rule:
    • $\frac{d}{dx}[f(g(x))]=f^{\prime }(g(x))\times g^{\prime }(x)$
  • integral of ln(x)

• Trig Functions, their equalities etc.

• Complex Trig functions and their simpler equivalent.

• Random ass equalities, eg. lim(sin(x)/x) = 1

  • lim(Sin(3x)/x)=3
  • lim(sin(x)/3x)=1/3
  • lim(x^2 * sin(1/x)) as x→0 =
  • Sigma Laws and useful facts to memorise
  • integral of sqrt(1+tan^2(x))
  • sin(x) < x for x > 0.
    • $\int e^x\cos (x)dx$
    • Solution → $\frac{e^x\sin (x)}{2}+\frac{e^x\cos (x)}{2}+C$ !!!!!!!!!!!!!!!!!!!!!!
    • $\int \frac{f^{\prime }(y)}{f(y)}dy=\ln |f(y)|$

• Common Convergent stuff like “we know that 1/t converges” etc.

• Convergence, Integral Test

• Alternating Series Test

• Ratio Test

• Convergence of Power Series

• Logs

• All of ln()‘s to be handy for instant Logarithmic Differentiation

• Formula for Washer, include outer=f(x) and inner=g(x)

• Formula for Arc Length

• All the Physics formulae

  • Think of all the stuff done in the Work Module Week 6
  • Center of Mass

• Completing the Square

• Integrating Discontinuous integrals

• For convergence: P - test

• Sec^2 identity

• Logistic Differential Equation

• First Order Linear Differential Equation**** (FOLDE)

• Something that tells me to add a damn C

• Solids of Revolutions

• Better Mathematics?

• Definition of critical points

• Linear Approximation

• Basic Geometry stuff - area of sphere etc.

  • Also basic physics stuff - Density, Weight, mass, momentsmoments etc.

• Half-life question - Week 6 Workshop

• Same for DiffEquation*** + How to solve (ie. either separable equations or FOLDE)

• Partial Fractions → + Partial Sums (week 9 workshop)

• Decimal Expansion (week 9 workshop)

• P Tests of funky fractions

• How power series are related to geometric series.