1. (C) Transformations 2. (C) Transformations Given that the graphy=f ( x ) can be sketches, then it is possible to build other sketches through appropriate transformations.…
1. (J) Other Graphs e.g. (i) (2003)The diagram shows the graph of y = f(x)Draw separate sketches of the graphs of the following; 2. 1 i y f x 3. 1 i …
1. (A) Features You ShouldNotice About A Graph 2. (A) Features You ShouldNotice About A Graph (1) Basic Curves 3. (A) Features You ShouldNotice About A Graph (1) Basic Curves…
1. (H)Graphs of the Form y f x nwhere n>1 and an integer The graph of y f x can be sketched by first drawing y f x n and…
(D) Addition & Subtraction of Ordinates (D) Addition & Subtraction of Ordinates y = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x) separately…
Trig Substitutions Trig Substitutions 22 xa tan use ax Trig Substitutions 22 xa tan use ax 22 xa cosor sin use axax Trig Substitutions…
1. Integration By Partial Fractions AxTo find; dx P x 2. Integration By Partial Fractions AxTo find; dx P x 1 If degA x degP…
1. Integration By Parts 2. Integration By PartsWhen an integral is a product of two functions and neither is thederivative of the other, we integrate by parts. 3. Integration…
1. Integration By Partial Fractions AxTo find; dx P x 2. Integration By Partial Fractions AxTo find; dx P x 1 If degA x degP…
1. Trig Integrals 2. Trig Integrals(1) Standard Integrals1 sin axdx a cos ax c 3. Trig Integrals(1) Standard Integrals1…
1. Integrating Quadratic Denominators1 2 dx 2 dxa xa x a…
1. Integration By Parts 2. Integration By PartsWhen an integral is a product of two functions and neither is thederivative of the other, we integrate by parts. 3. Integration…
Integration By Partial Fractions dxxP xA find; To Integration By Partial Fractions dxxP xA find; To divisionaperform,degdegIf1…
Integrating Quadratic Denominators axax dx ax dx xaxa dx xa dx 22 22 2 1 Integrating…
Reduction Formula Reduction Formula Reduction (or recurrence) formulae expresses a given integral as the sum of a function and a known integral. Integration by parts often…
1. Reduction Formula 2. Reduction FormulaReduction (or recurrence) formulae expresses a given integral asthe sum of a function and a known integral.Integration by parts often…
1. Integration By Parts 2. Integration By PartsWhen an integral is a product of two functions and neither is thederivative of the other, we integrate by parts. 3. Integration…
1. Odd & Even Functions(1) Even f x f x 2. Odd & Even Functions(1) Evenf …
X2 Graph Sketching 1 Review of Basic Transformations Translations: A graph may be translated by shifting it horizontally, vertically, or in both directions. When x is replaced…
CALCULUS Curve Sketching (V) 1. Consider the following polynomial function:f(x) = (x + 1)(x− 4) x Sketch the grapf of the function f(x) . 2. Consider the following polynomial…