Mathematics

Problem

The curve is given parametrically by

x = e^{kt}\cos t

and

y = e^{kt}\sin t

, where

k

is a real constant and

t

takes all real values. Answer the following questions: a. (i) Derive an expression for

\dfrac{d^{2}y}{dx^{2}}

in terms of

k

and

t

. b. (ii) Determine the condition on

k

for which

\dfrac{d^{2}y}{dx^{2}}>0

for every real

t

. c. (iii) For the value(s) of

k

obtained in part (ii), verify that the curve possesses no points of inflection.