Labware - MA35 Multivariable Calculus - Two Variable Calculus
 MA35 Labs 2 » Two Variable Calculus Contents2.1 Functions of Two Variables 2.1.1 Introduction 2.1.2 Linear Functions 2.1.4 Slice Curves 2.1.6 Continuity 2.4 Integration Search

Introduction (Page: Demo Tutorial | Functions )

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Calculus is the study of functions.

Demos

 Linear Functions This demo shows the linear function in two variables L(x,y) = px + qy +k over the rectangular domain 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. You can change the constants p,q and k using the respective red, blue or purple slide bar, and the Graph: L(x,y) window will show the function graph of L(x,y) with the chosen values for the constants. If you slide the hotspot on the purple slidebar, (thereby varying the constant k) the function graph is translated up and down in the directon of f(x,y). Varying p,and r on the red and blue slidebars will scale in the x- and y- direction of the graph.

Examples

The Zero Function

Constant Functions

Linear Functions

Exercises

• 1. Show that if p ≠ 0, then for every z there is a point (x,y) such that L(x,y) = px + qy + k = z. Show that if p = 0 but q ≠ 0, then the same result holds.
• 2. Consider the planar triangle with vertices at the x-intercept, y-intercept, and z-intercept points of the graph of L(x,y) = px + qy + k. For what values of p, q, and k does this triangle intersect the graph of L(x,y) over the domain 0 {leq} x {leq} 1, 0 {leq} y {leq} 1?