Mathematics

Problem

Let

x=f(t)

and

y=g(t)

represent a differentiable plane curve, with

t

a real parameter. a. (i) Obtain an expression for

\dfrac{dy}{dx}

in terms of

\dfrac{dx}{dt}

and

\dfrac{dy}{dt}

. b. (ii) Using the result of part (i), give a clear mathematical explanation of the conditions under which the tangent to the curve is (a) horizontal and (b) vertical. c. (iii) Justify why both conditions in part (ii) cannot hold simultaneously at a single regular point of the curve.

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