Hi, I'm working on MIT's Single Variable Calculus and this is from the Problem set 3:
My solutions:
a) (This should be correct)
\(\displaystyle x_3 = \frac{x_1x_2(y_2-y_1)}{x_1y_2-x_2y_1}\)
\(\displaystyle y_3 = \frac{y_1y_2(x_1-x_2)}{x_1y_2-x_2y_1}\)
b) (Correct?)
\(\displaystyle L_2\) has length 1: \(\displaystyle y_2^2+x_2^2=1\)
Then differentiating w.r.t. \(\displaystyle x_2\):
\(\displaystyle \frac{dy_2}{dx_2}=-\frac{x_2}{y_2}=-\frac{x_1 +\Delta x}{y_1 + \Delta y}\)
Is this equal to \(\displaystyle \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}\) ? I don't think so. How do I relate these two equations? Thanks
My solutions:
a) (This should be correct)
\(\displaystyle x_3 = \frac{x_1x_2(y_2-y_1)}{x_1y_2-x_2y_1}\)
\(\displaystyle y_3 = \frac{y_1y_2(x_1-x_2)}{x_1y_2-x_2y_1}\)
b) (Correct?)
\(\displaystyle L_2\) has length 1: \(\displaystyle y_2^2+x_2^2=1\)
Then differentiating w.r.t. \(\displaystyle x_2\):
\(\displaystyle \frac{dy_2}{dx_2}=-\frac{x_2}{y_2}=-\frac{x_1 +\Delta x}{y_1 + \Delta y}\)
Is this equal to \(\displaystyle \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}\) ? I don't think so. How do I relate these two equations? Thanks