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Home > Mathematics > Mathematics > Tangent to the Curve

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Tutorials

• Continuity of functions 
  A page with links to summaries related to continuity of functions.
• Definition of tangent (Java) 
  A synopsis of the derivative of a function with links to discussions and visual examples.
• Demonstation of tangent by zooming in 
  An animated presentation of approximating the slope of a tangent by zooming in at the point of contact.
• Differentiation using function of a function 
  A synopsis of the chain rule with some worked examples.
• Explore definition of continuity (piecewise function) with MathView 
  An animated demonstration of determining continuity of a function with links to explanations.
• Formal definition of limits 
  A page with links to summaries related to formal definition of functions.
• Limits 
  A page with links to summaries related to limits.
• Limits to infinity 
  A page with links to summaries related to limits to infinity.
• Problems with graphing piecewise functions 
  An animated investigation of continuity of a point by using a MathView tool. (MathView)
• Rules of differentiation 
  A page with links to summaries related to rules for differentiation.
• Tangent as the limit of secants 
  An animated investigation of the construction of a tangent line. (MathView)
• Tangent lines and the derivative 
  A page with links to summaries related to tangent lines and the derivative.
• Tangents as introduction to derivatives 
  A synopsis of the topic with links to other demonstrations and discussion pages.
• Using the definition of tangent for fractional indices 
  An algebraic and graphical demonstration of function which is not differentiable at a point. (MathView)
• Using the definition of tangent for quotient rule 
  A demonstration of finding a derivative from first principles. (MathView)
• Using the definition of tangent for radicals 
  A demonstration of finding a derivative from first principles. (MathView)

Assessment

• A set of HSC past papers & advice on the examination
  Hints and answers from past exam papers (formerly '2 Unit'), and past articles from Sydney Morning Herald advice to students.
• Drill questions for the chain rule (various functions) 
  A synopsis with a set of examples with links to discussion and drill questions.
• Drill questions for the product rule (various functions) 
  A synopsis with a set of examples with links to discussion and drill questions.
• Drill questions for the quotient rule (various functions) 
  A synopsis with a set of examples with links to discussion and drill questions.
• Evaluating limits 
  A quiz on limits with links to check the answer.
• Introductory calculus (T/F quiz) 
  A series of twenty true/false questions with answers provided,
• Quiz on mixed derivative of functions (various functions) 
  A series of sixty questions on differentiation with a score provided at the end.
• Quiz using definition of continuity 
  A series of seventy five questions on definition of continuity with a score provided at the end.

Resources

• Approximation for tangent at a point 
  An animated presentation of the tangent line to a function. (MathView)
• Definition of derivatives (Visicalc) 
  A synopsis with links to examples and discussion on the definition of derivatives.
• Derivative surfer (applet) 
  Brilliant applet demonstrating the effect of 'surfing the waves' of a curve to generate derivative values and the resultant graph.
• Differentials and differences 
  A synopsis with links to an animation presenting a tangent to a curve,
• Differentiation formulae  
  A synopsis of the rules of differentiation with links to discussion pages and examples.
• Dynamic examination of slope 
  A graphical illustration of the approximation of the tangent of a function.
• Example of application of chain rule 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of application of product rule 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of application of quotient rule 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of derivative of a sum 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of derivative of power rule 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of derivative of quadratic 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of derivative of quotient 
  An interactive presentation of differentiation from first principles. (MathView)
• Example of derivative of radical 
  An interactive presentation of differentiation from first principles. (MathView)
• Gathering evidence of horizontal asymptote 
  A tabulated illustration of determining the horizontal asymptote with links to instructions for graphics calculators.
• Horizontal asymptote 
  A graphical investigation of the limit of a function for varying values of coefficients. (MathView)
• How the ball bounces 
  Three brilliant animations exploring the graphical representation of a bouncing ball (consider continuity & differentiability).
• Introduction to limits 
  A synopsis with examples and links to exercises, drill questions and instructions for graphics calculators.
• Limits of x, sin x, tan x 
  Applet which explores visually and numerically the relationship between x in radians, sin x and tan x as x-> 0.
• Secants and tangents 
  A synopsis of tangents and the curve with a link to an animation illustrating the similarity of the two lines.
• Summary of the derivative 
  A synopsis of Introductory Calculus with links to a tutorial.
• The limit of sinx/x 
  A synopsis of the topic with links to graphical demonstration of the limit.
• Vertical asymptote 
  An animated presentation of the limiting value of a function as the value approaches the vertical aymptote. (MathView)
• Visually finding a tangent 
  An animated presentation of instructions to find the tangent lines on a graphics calculator. (Flash)
• Zooming in on a tangent (dynamic) 
  An animated demonstration of zooming in on a tangent at the point of contact.