Summary Test 2 Prep (MAM1000W)

The test will cover material from everything that wasn't covered in test 1 up to what was covered by the end of last term (excluding related rates), which corresponds to the coming week's homework. The detailed breakdown of it is as follows: • Inverse functions, logs and inverse trig functions (parts of Stewart 6.1,6.3 and 6.6) • Proof by contradiction (Resource book) • Proof by induction (Resource book) • The limit of a function (Stewart 1.5) • Calculating limits using the limit laws, and continuity (Stewart 1.6 and 1.8) • Limits involving infinity (Stewart 3.4) • Derivatives and rates of change (Stewart 2.1) • The derivative as a function (Stewart 2.2) • Differentiation formulas (Stewart 2.3) • Derivatives of trig functions (Stewart 2.4) • The chain rule (Stewart 2.5) • Implicit differentiation (Stewart 2.6) • Derivatives of exponential functions (Stewart 6.2) • Derivatives of log functions (Stewart 6.4) • Derivatives of inverse trig functions (Stewart 6.6) Proofs that you will be expected to know (though you could be asked to prove other things): • Differentiability implies continuity (Stewart 2.2, Theorem 4) • The Sum Rule (Stewart 2.3) • The Power Rule for the case when n is a positive integer (Stewart 2.3. You may not use logarithmic differentiation) • The Product Rule (Theorem 27 in the resource book) • lim_(θ-0) sin(θ)/θ = 1(Stewart 2.4. You may not use L'Hospital's Rule!) • d/dx (sin(x)) = cos(x) (Stewart 2.4. Using the previous result)