Is the following function continuous at x=2 ?
f\left(x\right)=\begin{cases} x^{2}-3x+5 \ \text{ if }\ x\leqslant2 \cr \cr \dfrac{x+13}{2x+1}\ \text{ if }\ x\gt2 \end{cases}
Is the following function continuous at x=3 ?
f\left(x\right)=\begin{cases} \sqrt{x^{2}+5x+12} \ \text{ if }\ x\leqslant3 \cr \cr 7x-15\ \text{ if }\ x\gt3 \end{cases}
Is the following function continuous at x=2 ?
f\left(x\right)=\begin{cases} \dfrac{\sin\left(x-2\right)}{x-2}\ \text{ if }\ x\lt2 \cr \cr \log_3\left(x^{2}-1\right)\ \text{ if }\ x\geqslant2 \end{cases}
Is the following function continuous at x=-1 ?
f\left(x\right)=\begin{cases} \dfrac{3x-5}{x-3}\ \text{ if }\ x\lt-1 \cr \cr x+3 \text{ if }\ x\geqslant-1 \end{cases}
Is the following function continuous at x=\dfrac{7\pi}{9} ?
f\left(x\right)=\begin{cases}\cos\left(3x-2\pi\right)\ \text{ if }\ x\lt\dfrac{7\pi}{9} \cr \cr \sin\left(\dfrac{9x}{7}\right)+\dfrac{1}{2}\text{ if }\ x\geqslant\dfrac{7\pi}{9} \end{cases}
Is the following function continuous at x=4 ?
f\left(x\right)=\begin{cases}\sqrt{2x+1} \text{ if }\ x\lt4\cr \cr \dfrac{5x+4}{x+2}\text{ if }\ x\geqslant4 \end{cases}
Is the following function continuous at x=1 ?
f\left(x\right)=\begin{cases}\dfrac{2x^{2}+3x-5}{x-6} \text{ if }\ x\lt1\cr \cr \ln\left(x\right)+3\text{ if }\ x\geqslant1 \end{cases}