Determine If Is Everywhere Continuous, and If Not, Locate the Point(s) of \begin{array}

question 237

Essay

Determine if $f ( x , y ) = \left\{ \begin{array} { l l } \frac { x ^ { 2 } + x y } { x ^ { 2 } + y ^ { 2 } } & \text { if } ( x , y ) \neq ( 0,0 ) \\1 & \text { if } ( x , y ) = ( 0,0 )\end{array} \right.$ is everywhere continuous, and if not, locate the point(s) of discontinuity.

---

Definitions:

Wire Connectors

Devices designed to join electrical conductors together, ensuring a secure and reliable electrical circuit.

Signal Path

The route or channel through which an electronic signal moves from one component to another within a system or circuit.

Add-on Instructions

Custom instructions created within a PLC program to encapsulate frequently used or complex logic.

Instruction Set

The set of general-purpose instructions available with a given controller. In general, different machines have different instruction sets.