Question

For the function f(x) =$\left( \cos\frac{\alpha}{r} + i\sin\frac{\alpha}{r} \right)$following are true

• A. Continuous at all points except at x = 1
• B. Differentiable at all points
• C. Differentiable at all points except at x = 1
• D. None of these

Answer 1

Answer: (C)

Differentiable at all points except at x = 1

Answer 2

f(x) =

f '(x) = $\left[ \begin{array} { c c c c } 0 & , & \mathrm { x } < 1 & \\ 0 & , & \mathrm { x } = 1 & \mathrm { f } ^ { \prime } \left( 1 ^ { - } \right) = 0 \\ 2 \mathrm { x } & , & \mathrm { x } > 1 & \mathrm { f } ^ { \prime } \left( 1 ^ { + } \right) = 2 \times 1 = 2 \end{array} \right.$

not diff. at x = 1