Show that the functions f(x) = 5x - \(\left| x \right| \) is continuous at x = 0

For what value of k, the following function is continous at x =0?
f(x) = \(\begin{cases} \frac { 1-cos4x }{ 8{ x }^{ 2 } } \quad ifx\neq 0 \\ k\quad \quad \quad ifx=0 \end{cases}\)

Show that the function f(x) = 5x -3 is continous at x = +3

Prove that the function given by f(x) = \(\left| x-1 \right| \), x \(\in\) R is not differentiable at x =1

Evaluate \(\underset { x\rightarrow \frac { 1 }{ 2 } }{ lim } \frac { { 4x }^{ 2 }-1 }{ 2x-1 } \)