Determine if the graph of the function $f\left(x\right)$is continuous and/or differentiable at $x=1$.

Which of the following equations represents the orthogonal trajectories of the family of curves given by $x^2+2y^2=k^2$?

Given the system of differential equations $\frac{dx}{dt}=2x+3y$ and $\frac{dy}{dt}=6x+5y$, which of the following is the general solution for $x\left(t\right)$ and $y\left(t\right)$?

Determine if the graph of the function $f\left(x\right)$is continuous and/or differentiable at $x=2$.

Determine if the graph of the function $f\left(x\right)$is continuous and/or differentiable at $x=1$.

Determine if the function$f\left(x\right)$ is continuous and/or differentiable at $x=3$.

Determine if the function$f\left(x\right)$ is continuous and/or differentiable at $x=2$.

Determine where the function $f\left(x\right)$ is not differentiable.

$f\left(x\right)=\frac{3}{x+2}$

Determine if the function$f\left(x\right)$ is continuous and/or differentiable at $x=3$.