If fixgy is continuous and X ₁3 path-connected, then so is f(x)

Give an example of an R²-valued function F with D(F) equal to an interval (a, b) and having the following properties: limb F(x) does not exist; limb || F(x)|| does exist. Is such an example possible in the R¹-setting?

Let g(x) = x2 – 4/x2 – 3x -10 Determine x-value(s) for which g is not continuous

Determine whether or not the following are continuous functions. Sketch the graph