1973 -

Given the curve $\displaystyle x + xy +2y^2 = 6$, find the coordinates of all other points on this curve with slop equal to the slope at (2,1)

1970 -

the function $\displaystyle f$ is defined for all x not equal to 0, in the interval $\displaystyle -1<x<1$ by $\displaystyle f(x)=\frac{x-\sin 2x}{\sin x}$

a) how should $\displaystyle f(0)$ be defined in order that $\displaystyle f$ be continuous for all x in the interval $\displaystyle -1<x<1$?

b) With $\displaystyle f(0)$ defined as in part a), use the definition of the derivative to determine whether $\displaystyle f'(0)$ exists. Show your work.

For 1973, ive been able to find the derivative as $\displaystyle \frac{dy}{dx} = \frac{-y-1}{x+4y}$. However, ive tried solving it with the original equation but cannot get an answer

For 1970, I've got $\displaystyle f(0) = -1$, but using the definition of the derivitive gets really really messy and i cant get the h to cancel out.

all help appreciated!!